Atangana-Baleanu fractional approach to the solutions of Bagley-Torvik and Painlevé equations in Hilbert space
From MaRDI portal
Publication:2201404
DOI10.1016/j.chaos.2018.10.013zbMath1442.65119OpenAlexW2898594805MaRDI QIDQ2201404
Omar Abu Arqub, Mohammed Al-Smadi
Publication date: 29 September 2020
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.chaos.2018.10.013
Painlevé equationreproducing kernel Hilbert space methodBagley-Torvik equationAtangana-Baleanu fractional derivative
Numerical methods for initial value problems involving ordinary differential equations (65L05) Fractional ordinary differential equations (34A08)
Related Items
Atangana-Baleanu fractional framework of reproducing kernel technique in solving fractional population dynamics system ⋮ Numerical approximation of fractional Burgers equation with Atangana-Baleanu derivative in Caputo sense ⋮ Modeling and analysis of the polluted lakes system with various fractional approaches ⋮ Operational matrix for Atangana-Baleanu derivative based on Genocchi polynomials for solving FDEs ⋮ Monotonically decreasing behavior of measles epidemic well captured by Atangana-Baleanu-Caputo fractional operator under real measles data of Pakistan ⋮ Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations ⋮ Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis ⋮ Framework for treating non-linear multi-term fractional differential equations with reasonable spectrum of two-point boundary conditions ⋮ Approximate solutions of Atangana-Baleanu variable order fractional problems ⋮ Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: theorems and applications ⋮ Numerical solutions of nonlinear fractional model arising in the appearance of the strip patterns in two-dimensional systems ⋮ Bifurcation phenomena in the peristaltic transport of non-Newtonian fluid with heat and mass transfer effects ⋮ Theoretical and semi-analytical results to a biological model under Atangana-Baleanu-Caputo fractional derivative ⋮ A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations ⋮ A mathematical model analysis of meningitis with treatment and vaccination in fractional derivatives ⋮ A novel method for nonlinear impulsive differential equations in broken reproducing kernel space ⋮ Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions ⋮ Mathematical analysis of dengue fever outbreak by novel fractional operators with field data ⋮ Delay-asymptotic solutions for the time-fractional delay-type wave equation ⋮ Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data ⋮ A comparative study of fractional-order diffusion model within Atangana-Baleanu-Caputo operator ⋮ Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators ⋮ Mathematical model for the novel coronavirus (<scp>2019‐nCOV</scp>) with clinical data using fractional operator ⋮ A new semi‐analytic solution of fractional sixth order<scp>Drinfeld–Sokolov–Satsuma–Hirota</scp>equation ⋮ 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 ⋮ Existence of solutions for a higher order Riemann–Liouville fractional differential equation by Mawhin's coincidence degree theory ⋮ Stochastic filtering in fractional-order circuits ⋮ Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense ⋮ Differential and integral operators with constant fractional order and variable fractional dimension ⋮ Modeling chickenpox disease with fractional derivatives: from Caputo to Atangana-Baleanu ⋮ Modeling attractors of chaotic dynamical systems with fractal-fractional operators ⋮ Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator ⋮ A novel method to solve variable-order fractional delay differential equations based in Lagrange interpolations ⋮ Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC fractional Volterra integro-differential equations ⋮ Two computational approaches for solving a fractional obstacle system in Hilbert space ⋮ An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative ⋮ Construction of fractional power series solutions to fractional stiff system using residual functions algorithm ⋮ Asymptotic-sequentially solution style for the generalized Caputo time-fractional Newell-Whitehead-Segel system ⋮ A different approach for study some fractional evolution equations ⋮ A novel technique for \((2 + 1)\)-dimensional time-fractional coupled Burgers equations ⋮ Finite element method for drifted space fractional tempered diffusion equation ⋮ On (s,t)-Volterra Quadratic Stochastic Operators of a Bisexual Population ⋮ Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation ⋮ Numerical solutions of hybrid fuzzy differential equations in a Hilbert space ⋮ A two-step improved Newton method to solve convex unconstrained optimization problems ⋮ Caputo fractional continuous cobweb models ⋮ Laguerre reproducing kernel method in Hilbert spaces for unsteady stagnation point flow over a stretching/shrinking sheet ⋮ A meshless local Galerkin method for solving Volterra integral equations deduced from nonlinear fractional differential equations using the moving least squares technique ⋮ On the numerical solution of a class of linear fractional integro-differential algebraic equations with weakly singular kernels ⋮ An adaptive numerical approach for the solutions of fractional advection-diffusion and dispersion equations in singular case under Riesz's derivative operator ⋮ Numerical Simulation of Nonlinear Ecological Models with Nonlocal and Nonsingular Fractional Derivative ⋮ Advanced analytical treatment of fractional logistic equations based on residual error functions ⋮ Fractional differential equations and Volterra-Stieltjes integral equations of the second kind ⋮ Analysis of complex time series based on EMD energy entropy plane ⋮ Numerical solutions of fractional delay differential equations using Chebyshev wavelet method ⋮ Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate ⋮ Solving Time-Space-Fractional Cauchy Problem with Constant Coefficients by Finite-Difference Method ⋮ MESHLESS GALERKIN METHOD BASED ON RBFS AND REPRODUCING KERNEL FOR QUASI-LINEAR PARABOLIC EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS ⋮ Optimal interpolation formulas with derivative in the space L(m)2(0,1) ⋮ Computing bifurcations behavior of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types in hilbert space with error analysis
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Volterra type
- Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations
- A novel expansion iterative method for solving linear partial differential equations of fractional order
- Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: a new iterative algorithm
- Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations
- A reproducing kernel method for solving nonlocal fractional boundary value problems
- New exact solutions of nonlinear fractional acoustic wave equations in ultrasound
- Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model
- Solution of fractional order system of Bagley-Torvik equation using evolutionary computational intelligence
- Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions
- On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
- General solution of the Bagley-Torvik equation with fractional-order derivative
- Reproducing kernel spaces and applications
- Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm
- Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems
- Wavelets optimization method for evaluation of fractional partial differential equations: an application to financial modelling
- A novel method for a fractional derivative with non-local and non-singular kernel
- Fractional derivatives with no-index law property: application to chaos and statistics
- Modified reproducing kernel method for singularly perturbed boundary value problems with a delay
- Representation of the exact solution for a kind of nonlinear partial differential equation
- Numerical algorithm for parabolic problems with non-classical conditions
- Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method
- Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method
- Solving a system of linear Volterra integral equations using the new reproducing kernel method
- On the new fractional derivative and application to nonlinear Baggs and Freedman model
- The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations
- A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation
- The numerical solution of the second Painlevé equation
- Residual Power Series Method for Fractional Diffusion Equations
- Numerical Computation of a Fractional Derivative with Non-Local and Non-Singular Kernel
- Numerical algorithm for solving time‐fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions
- Solutions of time‐fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space
- Approximate Solutions of DASs with Nonclassical Boundary Conditions using Novel Reproducing Kernel Algorithm
- Theory of Reproducing Kernels