On the generalized fractional derivatives and their Caputo modification

From MaRDI portal
Publication:4631150

DOI10.22436/jnsa.010.05.27zbMath1412.26006OpenAlexW2612981580MaRDI QIDQ4631150

Dumitru Baleanu, Fahd Jarad, Thabet Abdeljawad

Publication date: 24 April 2019

Published in: The Journal of Nonlinear Sciences and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.22436/jnsa.010.05.27


zbMATH Keywords

Caputo fractional derivativesHadamard fractional derivativesRiemann-Liouville fractional derivativesCaputo-Hadamard fractional derivativesgeneralized fractional integralgeneralized Caputo fractional derivatives


Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Fractional ordinary differential equations (34A08)


Related Items (only showing first 100 items - show all)

SIR epidemic model with Mittag-Leffler fractional derivative ⋮ Stability analysis for generalized fractional differential systems and applications ⋮ Analysis of fractional fishery model with reserve area in the context of time-fractional order derivative ⋮ New general Grüss-type inequalities over \(\sigma\)-finite measure space with applications ⋮ Existence and uniqueness results for \(\Phi\)-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition ⋮ Further results on existence of positive solutions of generalized fractional boundary value problems ⋮ Novel results on trapezoid-type inequalities for conformable fractional integrals ⋮ Some remarks on parameterized inequalities involving conformable fractional operators ⋮ Some new Gronwall-Bihari type inequalities associated with generalized fractional operators and applications ⋮ On \(\psi\)-Hilfer generalized proportional fractional operators ⋮ Stability analysis of boundary value problems for Caputo proportional fractional derivative of a function with respect to another function via impulsive Langevin equation ⋮ Fractional physical models based on falling body problem ⋮ Ostrowski type inequalities in the sense of generalized \(\mathcal{K}\)-fractional integral operator for exponentially convex functions ⋮ On a new class of fractional operators ⋮ Investigation of the \(p\)-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives ⋮ New results on Caputo fractional-order neutral differential inclusions without compactness ⋮ Multiple solutions for a class of boundary value problems of fractional differential equations with generalized Caputo derivatives ⋮ Stability results of positive solutions for a system of \(\psi \) -Hilfer fractional differential equations ⋮ Analysis of solutions of the integro-differential equations with generalized Liouville-Caputo fractional derivative by \(\rho\)-Laplace transform ⋮ Qualitative analysis of fractional relaxation equation and coupled system with \(\Psi\)-Caputo fractional derivative in Banach spaces ⋮ Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space ⋮ Novel improved fractional operators and their scientific applications ⋮ Numerical solutions of fractional optimal control with Caputo-Katugampola derivative ⋮ An analytical survey on the solutions of the generalized double-order \(\varphi\)-integrodifferential equation ⋮ Controllability of linear fractional systems with delay in control ⋮ Identification of fractional water transport model with \(\psi \)-Caputo derivatives using particle swarm optimization algorithm ⋮ Ulam stability for delay fractional differential equations with a generalized Caputo derivative ⋮ Accuracy and speed of splitting methods for three-dimensional space-time fractional diffusion equation with \(\psi\)-Caputo derivatives ⋮ Fractional operators with boundary points dependent kernels and integration by parts ⋮ Variational principles in the frame of certain generalized fractional derivatives ⋮ Generalized fractional derivatives and Laplace transform ⋮ Mittag-Leffler input stability of fractional differential equations and its applications ⋮ Fundamental results about the fractional integro-differential equation described with Caputo derivative ⋮ Analytical approximate solutions for differential equations with generalized Caputo-type fractional derivatives ⋮ Existence results for ψ–Caputo fractional neutral functional integro-differential equations with finite delay ⋮ On the Generalization of κ-Fractional Hilfer-Katugampola Derivative with Cauchy Problem ⋮ Unnamed Item ⋮ Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space ⋮ Study of a class of generalized multiterm fractional differential equations with generalized fractional integral boundary conditions ⋮ A viral co-infection model with general infection rate in deterministic and stochastic environments ⋮ On more general forms of proportional fractional operators ⋮ On the modeling and numerical discretizations of a chaotic system via fractional operators with and without singular kernels ⋮ A study on the new class of inequalities of midpoint-type and trapezoidal-type based on twice differentiable functions with conformable operators ⋮ Stability analysis of time‐fractional differential equations with initial data ⋮ Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives ⋮ An extensive study on parameterized inequalities for conformable fractional integrals ⋮ Solvability of an infinite system of fractional differential equations with \(p\)-Laplacian operator in a new tempered sequence space ⋮ Existence of Urysohn and Atangana-Baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators ⋮ Parallel finite-difference algorithms for three-dimensional space-fractional diffusion equation with \(\psi\)-Caputo derivatives ⋮ A Gronwall inequality and its applications to the Cauchy-type problem under \(\psi\)-Hilfer proportional fractional operators ⋮ Some new integral inequalities associated with generalized proportional fractional operators ⋮ Existence and stability analysis for Caputo generalized hybrid Langevin differential systems involving three-point boundary conditions ⋮ Representation of solutions for Sturm–Liouville eigenvalue problems with generalized fractional derivative ⋮ On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative ⋮ Unnamed Item ⋮ Analysis of the financial chaotic model with the fractional derivative operator ⋮ Oscillation of differential equations in the frame of nonlocal fractional derivatives generated by conformable derivatives ⋮ Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives ⋮ Fractional logistic models in the frame of fractional operators generated by conformable derivatives ⋮ Black-Scholes option pricing equations described by the Caputo generalized fractional derivative ⋮ New results on existence in the framework of Atangana-Baleanu derivative for fractional integro-differential equations ⋮ Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives ⋮ Hyers-Ulam stability and existence criteria for coupled fractional differential equations involving \(p\)-Laplacian operator ⋮ Existence results for a nonlinear coupled system involving both Caputo and Riemann-Liouville generalized fractional derivatives and coupled integral boundary conditions ⋮ Unnamed Item ⋮ On more general fractional differential equations involving mixed generalized derivatives with nonlocal multipoint and generalized fractional integral boundary conditions ⋮ Extremal solutions for generalized Caputo fractional differential equations with Steiltjes-type fractional integro-initial conditions ⋮ Analysis of a four-dimensional hyperchaotic system described by the Caputo-Liouville fractional derivative ⋮ On class of fractional-order chaotic or hyperchaotic systems in the context of the Caputo fractional-order derivative ⋮ Existence results for nonlinear fractional boundary value problem involving generalized proportional derivative ⋮ A numerical algorithm applied to free convection flows of the Casson fluid along with heat and mass transfer described by the Caputo derivative ⋮ Green's functions for boundary value problems of generalized fractional differential equations with p-Laplacian ⋮ On a Caputo-type fractional derivative ⋮ Unnamed Item ⋮ Stability analysis of generalized neutral fractional differential systems with time delays ⋮ Unnamed Item ⋮ COMPARISON THEOREMS FOR CAPUTO–HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS ⋮ Some qualitative analyses of neutral functional delay differential equation with generalized Caputo operator ⋮ A computational study of transmission dynamics for dengue fever with a fractional approach ⋮ Representations and properties of a new family of ω-Caputo fractional derivatives ⋮ Lyapunov type inequality in the frame of generalized Caputo derivatives ⋮ The non-uniqueness of solution for initial value problem of impulsive differential equations involving higher order Katugampola fractional derivative ⋮ The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives ⋮ On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals ⋮ A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative ⋮ On Grüss inequalities within generalized \(\mathcal{K}\)-fractional integrals ⋮ Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer-Katugampola fractional derivative ⋮ On the oscillation of kernel function dependent fractional integrodifferential equations ⋮ A study of fractional differential equations and inclusions involving generalized Caputo-type derivative equipped with generalized fractional integral boundary conditions ⋮ Taylor's formula involving generalized fractional derivatives ⋮ Generalized Liouville-Caputo fractional differential equations and inclusions with nonlocal generalized fractional integral and multipoint boundary conditions ⋮ Generalized Mittag-Leffler input stability of the fractional differential equations ⋮ On generalized fractional operators and a gronwall type inequality with applications ⋮ Mittag-Leffler stability, control, and synchronization for chaotic generalized fractional-order systems ⋮ ON FRACTIONAL DIFFERENTIAL INCLUSION PROBLEMS INVOLVING FRACTIONAL ORDER DERIVATIVE WITH RESPECT TO ANOTHER FUNCTION ⋮ ON THE WEIGHTED FRACTIONAL OPERATORS OF A FUNCTION WITH RESPECT TO ANOTHER FUNCTION ⋮ A study of boundary value problem for generalized fractional differential inclusion via endpoint theory for weak contractions ⋮ More properties of the proportional fractional integrals and derivatives of a function with respect to another function ⋮ On Hilfer generalized proportional fractional derivative ⋮ CHAOTIC BEHAVIOR OF FINANCIAL DYNAMICAL SYSTEM WITH GENERALIZED FRACTIONAL OPERATOR



Cites Work


This page was built for publication: On the generalized fractional derivatives and their Caputo modification

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:4631150&oldid=18812849"
Powered by MediaWiki