Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order

DOI10.1016/j.chaos.2020.109721zbMath1483.65108OpenAlexW3012298806MaRDI QIDQ2120523

Mohamed A. Abdelkawy, António M. Lopes, Mohammed M. Babatin

Publication date: 31 March 2022

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2020.109721

zbMATH Keywords

collocation methodfunctional differential equationCaputo fractional derivativeshifted fractional Jacobi-Gauss-Lobatto quadratureshifted fractional Jacobi-Gauss-Radau quadrature

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Functional-differential equations with fractional derivatives (34K37) Numerical methods for functional-differential equations (65L03)

Related Items (11)

A class of computational approaches for simulating fractional functional differential equations via Dickson polynomials ⋮ Robust spectral treatment for time-fractional delay partial differential equations ⋮ An efficient Jacobi spectral method for variable-order time fractional 2D Wu-Zhang system ⋮ Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains ⋮ Unnamed Item ⋮ Shifted Legendre spectral collocation technique for solving stochastic Volterra-Fredholm integral equations ⋮ Jacobi spectral method for variable-order fractional Benney-Lin equation arising in falling film problems ⋮ Fractional-order shifted Legendre collocation method for solving non-linear variable-order fractional Fredholm integro-differential equations ⋮ A fast collocation algorithm for solving the time fractional heat equation ⋮ Effective numerical technique for solving variable order integro-differential equations ⋮ Numerical simulation of time variable fractional order mobile-immobile advection-dispersion model based on an efficient hybrid numerical method with stability and convergence analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical analysis of a new space-time variable fractional order advection-dispersion equation
• A review of operational matrices and spectral techniques for fractional calculus
• A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations
• A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
• A finite difference technique for solving variable-order fractional integro-differential equations
• A new numerical method for variable order fractional functional differential equations
• A Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth-order differential equations
• Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes first problem for a heated generalized second grade fluid
• A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
• A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations
• A collocation method based on Jacobi and fractional order Jacobi basis functions for multi-dimensional distributed-order diffusion equations
• A spectral framework for fractional variational problems based on fractional Jacobi functions
• An efficient numerical method for variable order fractional functional differential equation
• A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
• Alternating direction implicit difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel
• Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: a fractional calculus approach
• A fractional quadratic autocatalysis associated with chemical clock reactions involving linear inhibition
• Collocation methods for fractional differential equations involving non-singular kernel
• New observations on optimal cancer treatments for a fractional tumor growth model with and without singular kernel
• Shifted Jacobi spectral-Galerkin method for solving hyperbolic partial differential equations
• A finite element approximation for a class of Caputo time-fractional diffusion equations
• Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain
• Shifted Jacobi-Gauss-collocation with convergence analysis for fractional integro-differential equations
• A new collection of real world applications of fractional calculus in science and engineering
• System of fractional differential algebraic equations with applications
• Analytical and numerical solutions of electrical circuits described by fractional derivatives
• An effective numerical method for solving nonlinear variable-order fractional functional boundary value problems through optimization technique
• Diabetes mellitus and TB co-existence: clinical implications from a fractional order modelling
• Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction-diffusion equations
• Second order accuracy finite difference methods for space-fractional partial differential equations
• A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations
• The solution of nonlinear ordinary differential equations in Chebyshev series
• An Optimization Wavelet Method for Multi Variable-order Fractional Differential Equations
• Numerical solutions of the fractional Fisher’s type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods
• New exact solution of generalized biological population model
• General Fractional Derivatives
• The Finite Difference Methods for Fractional Ordinary Differential Equations
• A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
• Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations
• Spectral Methods
• Chebyshev Collocation Methods for Ordinary Differential Equations
• Trigonometric Interpolation of Empirical and Analytical Functions

This page was built for publication: Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order