Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
From MaRDI portal
Publication:1772765
DOI10.1016/j.fss.2004.08.001zbMath1061.26024OpenAlexW2070545443MaRDI QIDQ1772765
Barnabás Bede, Sorin Gheorghe Gal
Publication date: 21 April 2005
Published in: Fuzzy Sets and Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.fss.2004.08.001
fuzzy-number-valued functionsgeneralized differentiabilityfuzzy partial differential equationsordinary fuzzy differential equations
Fuzzy real analysis (26E50) General theory for ordinary differential equations (34A99) General topics in partial differential equations (35A99)
Related Items
Fractional relaxation-oscillation differential equations via fuzzy variational iteration method ⋮ Impulsive hybrid interval-valued functional integro-differential equations ⋮ Quasi type 2 fuzzy differential equations ⋮ Fuzzy Laplace transform method for the Ulam stability of linear fuzzy differential equations of first order with constant coefficients ⋮ EXISTENCE CRITERIA FOR THE UNIQUE SOLUTION OF FIRST ORDER LINEAR FUZZY DIFFERENTIAL EQUATIONS ON THE SPACE OF LINEARLY CORRELATED FUZZY NUMBERS ⋮ New optimality conditions for multiobjective fuzzy programming problems ⋮ Optimal control of linear fuzzy time-variant controlled systems ⋮ Applications of generalized fixed points theorems to the existence of uncertain differential equations with finite delay ⋮ On Goursat problem for fuzzy random partial differential equations under generalized Lipschitz conditions ⋮ Unnamed Item ⋮ First order linear fuzzy differential equations with fuzzy variable coefficients ⋮ An efficient analytical-numerical technique for handling model of fuzzy differential equations of fractional-order ⋮ An estimation of the solution of hybrid fuzzy differential equations ⋮ On the properties of fuzzy differential equations under cross operations ⋮ Solutions of higher order linear fuzzy differential equations with interactive fuzzy values ⋮ Fuzzy fractional differential equations with the generalized Atangana-Baleanu fractional derivative ⋮ Fuzzy differential equations with Riemann-Liouville generalized fractional integrable impulses ⋮ Calculus for linearly correlated fuzzy number-valued functions ⋮ First-order linear fuzzy differential equations on the space of linearly correlated fuzzy numbers ⋮ Optimality conditions for fuzzy optimization in several variables under generalized differentiability ⋮ Sensitivity of option prices via fuzzy Malliavin calculus ⋮ Comparison between the linearly correlated difference and the generalized Hukuhara difference of fuzzy numbers ⋮ A straightforward approach for solving dual fuzzy linear systems ⋮ Calculus for fuzzy functions with strongly linearly independent fuzzy coefficients ⋮ New metric-based derivatives for fuzzy functions and some of their properties ⋮ Some notes on the switching points for the generalized Hukuhara differentiability of interval-valued functions ⋮ Suboptimal control of linear fuzzy systems ⋮ State feedback control for fractional differential equation system in the space of linearly correlated fuzzy numbers ⋮ New differentiability concepts for set-valued functions and applications to set differential equations ⋮ Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions ⋮ Fractional calculus of linear correlated fuzzy-valued functions related to Fréchet differentiability ⋮ Hyers-Ulam stability of fuzzy fractional Volterra integral equations with the kernel \(\psi\)-function via successive approximation method ⋮ Well-posedness and stability for fuzzy fractional differential equations ⋮ A NOVEL NUMERICAL METHOD FOR SOLVING FUZZY VARIABLE-ORDER DIFFERENTIAL EQUATIONS WITH MITTAG-LEFFLER KERNELS ⋮ Stability result for fractional fuzzy neutral integro-differential equations ⋮ Interval variational inequalities and their relationship with interval optimization problems ⋮ A multi-step method to solve bipolar-fuzzy initial value problem ⋮ Fuzzy Fractional Equation with Derivative of Atangana-Baleanu and Fuzzy Semigroup ⋮ Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability ⋮ Adaptation of kernel functions‐based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations ⋮ Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator ⋮ A fuzzy solution of wave equation by <scp>FFS‐transform</scp> ⋮ \(L\)-fuzzy fixed point results in \(\mathcal{F}\)-metric spaces with applications ⋮ \(\mathrm{Z}^+\)-Laplace transforms and \(\mathrm{Z}^+\)-differential equations of the arbitrary-order, theory and applications ⋮ A modified reproducing Kernel Hilbert space method for solving fuzzy fractional integro-differential equations ⋮ Synchronization of fuzzy-chaotic systems with Z-controller in secure communication ⋮ Discrete fractional calculus for fuzzy-number-valued functions and some results on initial value problems for fuzzy fractional difference equations ⋮ GENERAL SOLUTION OF BASSET EQUATION WITH CAPUTO GENERALIZED HUKUHARA DERIVATIVE ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Runge-Kutta method of order four for solving fuzzy delay differential equations under generalized differentiability ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation ⋮ Solving fuzzy fractional differential equations using fuzzy Sumudu transform ⋮ A study on the differential and sub-differential of fuzzy mapping and its application problem ⋮ A version of the Stone-Weierstrass theorem in fuzzy analysis ⋮ Unnamed Item ⋮ Numerical solution of Abel's general fuzzy linear integral equations by fractional calculus method ⋮ On the existence of generalized weak solutions to discontinuous fuzzy differential equations ⋮ Unnamed Item ⋮ Solution of Fuzzy Heat Equation Under Fuzzified Thermal Diffusivity ⋮ Asymptotic solutions of fractional interval differential equations with nonsingular kernel derivative ⋮ Notes on fuzzy fractional Sumudu transform ⋮ Unnamed Item ⋮ The Generalized Solution for Initial Problems of Fuzzy Discontinuous Differential Equations ⋮ Toward the existence and uniqueness of solutions for fractional integro-differential equations under uncertainty ⋮ Fuzzy Noise-Induced Codimension-Two Bifurcations Captured by Fuzzy Generalized Cell Mapping with Adaptive Interpolation ⋮ Unnamed Item ⋮ SOLVING THE FUZZY INITIAL VALUE PROBLEM WITH NEGATIVE COEFFICIENT BY USING FUZZY LAPLACE TRANSFORM ⋮ Some results on the fundamental concepts of fuzzy set theory in intuitionistic fuzzy environment by using α and β cuts ⋮ On interval-valued invex mappings and optimality conditions for interval-valued optimization problems ⋮ Asymptotic behavior of \(C^0\)-solutions of evolution equations with uncertainties ⋮ On fuzzy improper integral and its application for fuzzy partial differential equations ⋮ Complete controllability of fuzzy fractional evolutions equation under Fréchet derivative in linear correlated fuzzy spaces ⋮ An estimation of the solution of first order fuzzy differential equations ⋮ Single level constraint interval arithmetic ⋮ Solution of linear differential equations with fuzzy boundary values ⋮ Generalized fuzzy differentiability with LU-parametric representation ⋮ Interval-valued functional differential equations under dissipative conditions ⋮ Periodic boundary value problems for impulsive fuzzy differential equations ⋮ Monotone method for fuzzy differential equations ⋮ Existence and uniqueness of solutions to the second order fuzzy dynamic equations on time scales ⋮ On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem ⋮ Nonlinear fuzzy differential equation with time delay and optimal control problem ⋮ The Cauchy type problem for interval-valued fractional differential equations with the Riemann-Liouville gH-fractional derivative ⋮ Existence and uniqueness results for fractional differential equations with uncertainty ⋮ KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions ⋮ Solution of fuzzy differential equations using fuzzy Sumudu transforms ⋮ Different solution strategies for solving epidemic model in imprecise environment ⋮ Global existence of solutions for interval-valued second-order differential equations under generalized Hukuhara derivative ⋮ Numerical solution of first-order linear differential equations in fuzzy environment by Runge-Kutta-Fehlberg method and its application ⋮ Calculus of fuzzy functions on time scales. I ⋮ Solving fuzzy differential equations based on the length function properties ⋮ A new study on first-order fuzzy Fredholm-Volterra integro-differential equations by Jacobi polynomials and collocation methods ⋮ Computational optimization of residual power series algorithm for certain classes of fuzzy fractional differential equations ⋮ A new approach for solving a class of fuzzy optimal control systems under generalized Hukuhara differentiability ⋮ On solutions to set-valued and fuzzy stochastic differential equations ⋮ Fuzzy bang-bang control problem under granular differentiability ⋮ Fuzzy stochastic differential equations driven by semimartingales-different approaches ⋮ Existence, uniqueness, and characterization theorems for nonlinear fuzzy integrodifferential equations of Volterra type ⋮ On fuzzy portfolio selection problems: a parametric representation approach ⋮ Methods in ranking fuzzy numbers: a unified index and comparative reviews ⋮ On the Ulam stability of first order linear fuzzy differential equations under generalized differentiability ⋮ First order linear fuzzy differential equations under generalized differentiability ⋮ On the existence of solutions to periodic boundary value problems for fuzzy linear differential equations ⋮ Calculus for interval-valued functions using generalized Hukuhara derivative and applications ⋮ Global existence of solutions for fuzzy second-order differential equations under generalized \(H\)-differentiability ⋮ Symmetric fuzzy numbers and additive equivalence of fuzzy numbers ⋮ A new approach to fuzzy initial value problem ⋮ A Schauder fixed point theorem in semilinear spaces and applications ⋮ Laplace transform formula on fuzzy \(n\)th-order derivative and its application in fuzzy ordinary differential equations ⋮ Solving nonlinear fuzzy differential equations by using fuzzy variational iteration method ⋮ The use of airfoil and Chebyshev polynomials methods for solving fuzzy Fredholm integro-differential equations with Cauchy kernel ⋮ The middle-parametric representation of fuzzy numbers and applications to fuzzy interpolation ⋮ Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations ⋮ Random fuzzy differential equations under generalized Lipschitz condition ⋮ Euler method for solving hybrid fuzzy differential equation ⋮ On the topological equivalence of some fuzzy flows near hyperbolic equilibria ⋮ Solving hybrid fuzzy differential equations by Chebyshev wavelet ⋮ Variation of constant formula for first order fuzzy differential equations ⋮ Fuzzy transforms of higher order approximate derivatives: A theorem ⋮ Solving fuzzy fractional differential equations by fuzzy Laplace transforms ⋮ Numerical solutions for linear system of first-order fuzzy differential equations with fuzzy constant coefficients ⋮ A new method for solving fuzzy linear differential equations ⋮ Some topological properties of solutions to fuzzy differential systems ⋮ Fuzzy logic-based generalized decision theory with imperfect information ⋮ An eigenvalue-eigenvector method for solving a system of fractional differential equations with uncertainty ⋮ Numerical solution of second-order fuzzy differential equation using improved Runge-Kutta Nyström method ⋮ On new solutions of fuzzy differential equations ⋮ Global existence of solutions for interval-valued integro-differential equations under generalized \(H\)-differentiability ⋮ Controllability of second-order semilinear fuzzy integrodifferential control systems with nonlocal initial conditions ⋮ Ostrowski type inequalities and applications in numerical integration for interval-valued functions ⋮ On the existence and uniqueness of solutions for fuzzy fractional differential equations ⋮ Global solutions of fuzzy integro-differential equations under generalized differentiability by the method of upper and lower solutions ⋮ A boundary value problem for second order fuzzy differential equations ⋮ On fuzzy solutions for heat equation based on generalized Hukuhara differentiability ⋮ Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles ⋮ Random fuzzy fractional integral equations -- theoretical foundations ⋮ Fractional calculus for interval-valued functions ⋮ Fuzzy differential equation with completely correlated parameters ⋮ Third-order three-point fuzzy boundary value problems ⋮ A generalization of Hukuhara difference and division for interval and fuzzy arithmetic ⋮ Generalized derivative and \(\pi \)-derivative for set-valued functions ⋮ Solutions of fuzzy differential equations based on generalized differentiability ⋮ Existence theorems for solutions to random fuzzy differential equations ⋮ System of differential equation with initial value as triangular intuitionistic fuzzy number and its application ⋮ Solution of second order linear fuzzy ordinary differential equation by Lagrange multiplier method with application in mechanics ⋮ A quasi-Newton method with rank-two update to solve fuzzy optimization problems ⋮ Runge-Kutta method for solving fuzzy differential equations under generalized differentiability ⋮ Some integral inequalities for interval-valued functions ⋮ Fuzzy delay differential equations under generalized differentiability ⋮ A new method for solving differential equations with vague parameters ⋮ Existence of local and global solutions of fuzzy delay differential inclusions ⋮ Sheaf fuzzy problems for functional differential equations ⋮ Solving second-order fuzzy differential equations by the fuzzy Laplace transform method ⋮ On the solutions for box differential equations under generalized Hukuhara derivative ⋮ Toward the existence and uniqueness of solutions of second-order fuzzy differential equations ⋮ Initial value problem for fuzzy differential equations under dissipative conditions ⋮ Solving fuzzy differential equations by differential transformation method ⋮ Generalized Hukuhara differentiability of interval-valued functions and interval differential equations ⋮ New results on multiple solutions for \(N\)th-order fuzzy differential equations under generalized differentiability ⋮ Numerical solution of fuzzy differential equations under generalized differentiability ⋮ Comparation between some approaches to solve fuzzy differential equations ⋮ The controlled convergence theorems for the strong Henstock integrals of fuzzy-number-valued functions ⋮ On a class of fuzzy functional differential equations ⋮ Notes on fuzzy complex analysis ⋮ On the stability of fuzzy linear dynamical systems ⋮ Some solving methods for a fuzzy multi-point boundary value problem ⋮ On the initial value problem for fuzzy differential equations of non-integer order \(\alpha \in (1,2)\) ⋮ On random fuzzy differential equations ⋮ Complete controllability for a class of fractional evolution equations with uncertainty ⋮ On the fuzzy fractional differential equation with interval Atangana-Baleanu fractional derivative approach ⋮ Spline collocation methods for systems of fuzzy fractional differential equations ⋮ Study of hybrid orthonormal functions method for solving second kind fuzzy Fredholm integral equations ⋮ On the linear fuzzy model associated with Caputo-Fabrizio operator ⋮ Existence and uniqueness solutions of fuzzy integration-differential mathematical problem by using the concept of generalized differentiability ⋮ Some fuzzy-interval integral inequalities for harmonically convex fuzzy-interval-valued functions ⋮ Fuzzy-interval inequalities for generalized preinvex fuzzy interval valued functions ⋮ Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: theorems and applications ⋮ An efficient numerical method for solving \(m\)-polar fuzzy initial value problems ⋮ New Hermite-Hadamard inequalities in fuzzy-interval fractional calculus via exponentially convex fuzzy interval-valued function ⋮ A fuzzy generalized power series method under generalized Hukuhara differentiability for solving fuzzy Legendre differential equation ⋮ Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions ⋮ Fuzzy fractional functional integral and differential equations ⋮ On fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings ⋮ A note on the generalized difference and the generalized differentiability ⋮ On the Newton method for solving fuzzy optimization problems ⋮ A new fuzzy approximation method to Cauchy problems by fuzzy transform ⋮ Characterizations of generalized differentiable fuzzy functions ⋮ Relationship between Bede-Gal differentiable set-valued functions and their associated support functions ⋮ On fuzzy differential equations in the quotient space of fuzzy numbers ⋮ Ill-posed fuzzy initial-boundary value problems based on generalized differentiability and regularization ⋮ On the solutions to first order linear fuzzy differential equations ⋮ Necessary and sufficient conditions for fuzzy optimality problems ⋮ Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses ⋮ Explicit solutions of fractional differential equations with uncertainty ⋮ A Jacobi operational matrix for solving a fuzzy linear fractional differential equation ⋮ A novel approach to approximate fractional derivative with uncertain conditions ⋮ Controlled convergence theorems for infinite dimension Henstock integrals of fuzzy valued functions based on weak equi-integrability ⋮ Numerical solutions of fuzzy differential equations by an efficient Runge-Kutta method with generalized differentiability ⋮ A parametrized sum of fuzzy numbers with applications to fuzzy initial value problems ⋮ Cubic interpolation: a line search technique for fuzzy optimization problems ⋮ Interval Abel integral equation ⋮ A reproducing kernel method for solving nonlocal fractional boundary value problems with uncertainty ⋮ Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems ⋮ Newton method for solving the multi-variable fuzzy optimization problem ⋮ Applications of fuzzy Laplace transforms ⋮ Interval-valued functional integro-differential equations ⋮ Random fuzzy differential equations with impulses ⋮ Solvability and stability of impulsive set dynamic equations on time scales ⋮ Approximating the solution of the linear and nonlinear fuzzy Volterra integrodifferential equations using expansion method ⋮ Fuzzy integral equations and strong fuzzy Henstock integrals ⋮ A survey on fuzzy fractional differential and optimal control nonlocal evolution equations ⋮ Generalized convexity in fuzzy vector optimization through a linear ordering ⋮ Hyers-Ulam-Rassias stability of first order linear partial fuzzy differential equations under generalized differentiability ⋮ The initial value problem for interval-valued second-order differential equations under generalized H-differentiability ⋮ Solution method for a boundary value problem with fuzzy forcing function ⋮ Optimality conditions for generalized differentiable interval-valued functions ⋮ On periodic solutions to first order linear fuzzy differential equations under differential inclusions' approach ⋮ Homotopy analysis method for fuzzy Boussinesq equation ⋮ Almost periodicity of set-valued functions and set dynamic equations on time scales ⋮ Continuous solutions to a class of first-order fuzzy differential equations with discontinuous coefficients ⋮ The Cauchy problem of fuzzy differential equations under generalized differentiability ⋮ Oscillation property for fuzzy delay differential equations ⋮ On invex fuzzy mappings and fuzzy variational-like inequalities ⋮ Interval Cauchy problem with a second type Hukuhara derivative ⋮ Approximate solution of fuzzy differential equations under generalized differentiability ⋮ Fuzzy differential equations with interactive derivative ⋮ A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform ⋮ An operational matrix based on Legendre polynomials for solving fuzzy fractional-order differential equations ⋮ On solutions of linear fractional differential equations with uncertainty ⋮ Ostrowski-type inequalities for fuzzy-valued functions and its applications in quadrature theory ⋮ Solving interactive fuzzy initial value problem via fuzzy Laplace transform ⋮ Criterion for generalized weakly fuzzy invex monotonocities ⋮ A study of the impact of underground economy on integral tax burden in the proportional growth model under uncertainty ⋮ Quadratic interpolation technique to minimize univariable fuzzy functions ⋮ Discussion on proportional harvesting model in fuzzy environment: fuzzy differential equation approach ⋮ On strongly generalized preinvex fuzzy mappings ⋮ Wirtinger-type integral inequalities for interval-valued functions ⋮ On the solutions of first-order linear impulsive fuzzy differential equations ⋮ Ulam type stability of first-order linear impulsive fuzzy differential equations ⋮ A survey on the initial value problems of fuzzy implicit fractional differential equations ⋮ Interval optimal control for uncertain problems ⋮ A numerical method to solve a fuzzy differential equation via differential inclusions ⋮ A new derivative concept for set-valued and fuzzy-valued functions. Differential and integral calculus in quasilinear metric spaces ⋮ Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative ⋮ The Karush-Kuhn-Tucker optimality conditions for fuzzy optimization problems ⋮ A foundation on semigroups of operators defined on the set of triangular fuzzy numbers and its application to fuzzy fractional evolution equations ⋮ On the fuzzy Poisson equation ⋮ A new approach to linear interval differential equations as a first step toward solving fuzzy differential ⋮ Completeness, metrizability and compactness in spaces of fuzzy-number-valued functions ⋮ Initial value problem for second-order random fuzzy differential equations ⋮ Multiple solutions of ordinary differential systems with min-max terms and applications to the fuzzy differential equations ⋮ Fuzzy differential equation with nonlocal conditions and fuzzy semigroup ⋮ Properties of interval-valued function space under the gH-difference and their application to semi-linear interval differential equations ⋮ Solving a nonhomogeneous linear system of interval differential equations ⋮ Banach spaces generated by strongly linearly independent fuzzy numbers ⋮ Impulsive coupled system of fractional differential equations with Caputo-Katugampola fuzzy fractional derivative ⋮ Conditions for the existence of basic solutions of linear multivalued differential equations ⋮ Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations ⋮ Study of fuzzy fractional nonlinear equal width equation in the sense of novel operator ⋮ Solution to the Bessel differential equation with interactive fuzzy boundary conditions ⋮ Existence and uniqueness for fuzzy differential equation with Hilfer-Katugampola fractional derivative ⋮ Local and global existence and uniqueness of solution for class of fuzzy fractional functional evolution equation ⋮ Initial value problems in type-2 fuzzy environment ⋮ A new Jacobi tau method for fuzzy fractional Fredholm nonlinear integro-differential equations ⋮ Generalized Hukuhara-Clarke derivative of interval-valued functions and its properties ⋮ Modeling the linear drag on falling balls via interactive fuzzy initial value problem ⋮ Comparison of fuzzy Adomian decomposition method with fuzzy VIM for solving fuzzy heat-like and wave-like equations with variable coefficients ⋮ Controllability of Sobolev type fuzzy differential equation with non-instantaneous impulsive condition ⋮ Stable equilibrium configuration of two bar truss by an efficient nonmonotone global Barzilai-Borwein gradient method in a fuzzy environment ⋮ Fuzzy differential equations and the extension principle ⋮ Solving fuzzy fractional differential equations by a generalized differential transform method ⋮ Fuzzy Laplace transforms ⋮ Applications of contractive-like mapping principles to fuzzy fractional integral equations with the kernel \(\psi \)-functions ⋮ Analytical fuzzy triangular solutions of the wave equation ⋮ Solving fuzzy \((1+ n)\)-dimensional Burgers' equation ⋮ On the semigroup approach to the interval-valued differential evolution equations ⋮ Generalized Hukuhara Gâteaux and Fréchet derivatives of interval-valued functions and their application in optimization with interval-valued functions ⋮ An equivalence lemma for a class of fuzzy implicit integro-differential equations ⋮ Comments on ``A novel approach to approximate fractional derivative with uncertain conditions ⋮ Generalized differentiability and integrability for fuzzy set-valued functions on time scales ⋮ Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method ⋮ A numerical method for solving first-order fully fuzzy differential equation under strongly generalized H-differentiability ⋮ An extension of the Carathéodory differentiability to set-valued maps ⋮ A modified Euler method for solving fuzzy differential equations under generalized differentiability ⋮ Notes on local and nonlocal intuitionistic fuzzy fractional boundary value problems with Caputo fractional derivatives ⋮ On fuzzy Volterra-Fredholm integrodifferential equation associated with Hilfer-generalized proportional fractional derivative ⋮ General forms of solutions for linear impulsive fuzzy dynamic equations on time scales ⋮ Three-step averaging scheme for set-valued differential equations with generalized derivative ⋮ Almost periodic fuzzy multidimensional dynamic systems and applications on time scales ⋮ Practical stability of fuzzy differential equations with the second type of Hukuhara derivative ⋮ The Cauchy problem for quaternion fuzzy fractional differential equations ⋮ Solution of initial-value problem for linear third-order fuzzy differential equations ⋮ Multi-step \(gh\)-difference-based methods for fuzzy differential equations ⋮ Existence of fuzzy fractional stochastic differential system with impulses ⋮ Fuzzy fixed point results in \(\mathcal{F}\)-metric spaces with applications ⋮ A study of some properties of fuzzy Laplace transform with their applications in solving the second-order fuzzy linear partial differential equations ⋮ Fourth Order Runge-Kutta Method for Solving First-order Fully Fuzzy Differential Equations Under Strongly Generalized H-differentiability ⋮ An Allee threshold model for a Glioblastoma (GB)-immune system (IS) interaction with fuzzy initial values ⋮ Hukuhara difference of Z-numbers ⋮ Important notes for a fuzzy boundary value problem ⋮ \(M\)-fractional derivative under interval uncertainty: theory, properties and applications ⋮ Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator ⋮ Fuzzy optimal harvesting of a prey-predator model in the presence of toxicity with prey refuge under imprecise parameters ⋮ A perturbed collage theorem and its application to inverse interval integral problems ⋮ A note on generalized convexity for fuzzy mappings through a linear ordering ⋮ Analytical and numerical solutions of fuzzy differential equations ⋮ On linear fuzzy differential equations by differential inclusions' approach ⋮ A new membership function approach to uncertain functions ⋮ A fixed point approach to the Ulam stability of fuzzy differential equations under generalized differentiability ⋮ Two-point boundary value problems for first-order nonlinear fuzzy differential equation1 ⋮ Existence of extremal solutions for interval-valued functional integro-differential equations ⋮ A full fuzzy method for solving differential equation based on Taylor expansion ⋮ The fuzzy dynamic programming problems ⋮ Monotone iterative method for boundary value problems of fuzzy differential equations1 ⋮ A STUDY OF BIFURCATION OF PREY–PREDATOR MODEL WITH TIME DELAY AND HARVESTING USING FUZZY PARAMETERS ⋮ The Cauchy problems for discontinuous fuzzy systems under generalized differentiability ⋮ On generalized solutions for discontinuous fuzzy differential equations and strong fuzzy Henstock integrals ⋮ INVENTORY MODEL WITH DEMAND AS TYPE-2 FUZZY NUMBER: A FUZZY DIFFERENTIAL EQUATION APPROACH ⋮ FUZZY INCLUSION LINEAR SYSTEMS ⋮ On interactive fuzzy solutions for mechanical vibration problems ⋮ Homotopy analysis Shehu transform method for solving fuzzy differential equations of fractional and integer order derivatives ⋮ A Runge-Kutta numerical method to approximate the solution of bipolar fuzzy initial value problems ⋮ Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm integral equations ⋮ Comparison results for fuzzy differential equations ⋮ On fuzzy boundary value problems ⋮ Fuzzy approximate solutions of second-order fuzzy linear boundary value problems ⋮ Conditions for the existence of local solutions of set-valued differential equations with generalized derivative ⋮ A note on ``Two-point boundary value problems associated with non-linear fuzzy differential equations ⋮ Artificial neural network approach for solving fuzzy differential equations ⋮ A survey on fuzzy fractional variational problems ⋮ Application of fuzzy Picard method for solving fuzzy quadratic Riccati and fuzzy Painlevé I equations ⋮ \(q\)-fractional differential equations with uncertainty ⋮ A new efficient method using Fibonacci polynomials for solving of first-order fuzzy Fredholm-Volterra integro-differential equations ⋮ Differentiability of type-2 fuzzy number-valued functions ⋮ Type-2 fuzzy fractional derivatives ⋮ A new gH-difference for multi-dimensional convex sets and convex fuzzy sets ⋮ SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS ⋮ An analytical numerical method for solving fuzzy fractional Volterra integro-differential equations ⋮ Existence-uniqueness of solutions for fuzzy nabla initial value problems on time scales ⋮ On fuzzy type-1 and type-2 stochastic ordinary and partial differential equations and numerical solution ⋮ A semianalytical method for fuzzy integro-differential equations under generalized Seikkala derivative ⋮ Application of fuzzy fractional kinetic equations to modelling of the acid hydrolysis reaction ⋮ Constructive existence of (1,1)-solutions to two-point value problems for fuzzy linear multiterm fractional differential equations ⋮ Fuzzy solution of homogeneous heat equation having solution in Fourier series form ⋮ Existence and continuous dependence on initial data of solution for initial value problem of fuzzy multiterm fractional differential equation ⋮ Approximate solution of time-fractional fuzzy partial differential equations ⋮ Fuzzy delay differential equations under granular differentiability with applications ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equation ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fuzzy Laplace transform based on the Henstock integral and its applications in discontinuous fuzzy systems ⋮ Opial-type inequalities for interval-valued functions ⋮ Karush-Kuhn-Tucker conditions for interval and fuzzy optimization in several variables under total and directional generalized differentiability ⋮ Optimality conditions for fuzzy constrained programming problems ⋮ Minimum stability control problem and time-optimal control problem for fuzzy linear control systems ⋮ Calculus of fuzzy vector-valued functions and almost periodic fuzzy vector-valued functions on time scales ⋮ Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach ⋮ Differential calculus of fuzzy multi-variable functions and its applications to fuzzy partial differential equations ⋮ On retarded fuzzy functional differential equations and nonabsolute fuzzy integrals ⋮ An existence and uniqueness result for fuzzy Goursat partial differential equation ⋮ Fuzzy Volterra integro-differential equations using general linear method ⋮ LINEAR FIRST-ORDER FUZZY DIFFERENTIAL EQUATIONS ⋮ Existence of solutions for implicit fuzzy differential inclusions ⋮ A new approach for the optimal fuzzy linear time invariant controlled system with fuzzy coefficients ⋮ Existence and uniqueness results for fuzzy linear differential-algebraic equations ⋮ Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mareš equivalence relation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Brief note on the variation of constants formula for fuzzy differential equations
- Differentials of fuzzy functions
- On the fuzzy initial value problem
- Remarks on Peano-like theorems for fuzzy differential equations
- Introduction to fuzzy partial differential equations
- Towards the theory of fuzzy differential equations
- Almost periodic fuzzy-number-valued functions
- Approximate solutions, existence, and uniqueness of the Cauchy problem of fuzzy differential equations
- Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations
- An Approach to Modelling and Simulation of Uncertain Dynamical Systems
- Fuzzy sets
- Fuzzy differential equations
- On Henstock integral of fuzzy-number-valued functions. I
- Fuzzy initial value problem for \(N\)th-order linear differential equations