Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations

DOI10.1515/ijnsns-2020-0124OpenAlexW3138170664WikidataQ115236196 ScholiaQ115236196MaRDI QIDQ2698676

Waleed M. Abd-Elhameed, Youssri H. Youssri, José António Tenreiro Machado

Publication date: 24 April 2023

Published in: International Journal of Nonlinear Sciences and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ijnsns-2020-0124

zbMATH Keywords

Chebyshev polynomialshypergeometric functionsfractional differential equationstau methodduplication formula

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Linear functional-differential equations (34K06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Special sequences and polynomials (11B83) Fractional ordinary differential equations (34A08)

Related Items (7)

New fractional derivative expression of the shifted third-kind Chebyshev polynomials: application to a type of nonlinear fractional pantograph differential equations ⋮ A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley-Torvik differential equation ⋮ Advanced shifted sixth-kind Chebyshev tau approach for solving linear one-dimensional hyperbolic telegraph type problem ⋮ Enhanced shifted Tchebyshev operational matrix of derivatives: two spectral algorithms for solving even-order BVPs ⋮ Comparative work for the source identification in parabolic inverse problem based on Taylor and Chebyshev wavelet methods ⋮ Unnamed Item ⋮ Spectral treatment of one and two dimensional second-order BVPs via certain modified shifted Chebyshev polynomials

Uses Software

• SumTools

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of fractional pantograph differential equations by using generalized fractional-order Bernoulli wavelet
• Collocation for high order differential equations with two-points Hermite boundary conditions
• Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method
• The Legendre wavelet method for solving fractional differential equations
• A tau approach for solution of the space fractional diffusion equation
• The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
• On linearization coefficients of Jacobi polynomials
• Jacobi collocation approximation for solving multi-dimensional Volterra integral equations
• Numerical treatment of the fractional modeling on susceptible-infected-recovered equations with a constant vaccination rate by using GEM
• Sixth-kind Chebyshev spectral approach for solving fractional differential equations
• Generalized Lucas polynomial sequence approach for fractional differential equations
• A generalized fractional-order Legendre wavelet Tau method for solving fractional differential equations
• Time-fractional dependence of the shear force in some beam type problems with negative Young modulus
• Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations
• Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations
• On the mathematical modeling of soccer dynamics
• On the coefficients of integrated expansions and integrals of Chebyshev polynomials of third and fourth kinds
• Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models
• Numerical solution of mixed-type fractional functional differential equations using modified Lucas polynomials
• Solving a multi-order fractional differential equation using Adomian decomposition
• The special functions and their approximations. Vol. I, II
• Orthogonal polynomials, biorthogonal polynomials and spline functions
• On Solving Linear and Nonlinear Sixth-Order Two PointBoundary Value Problems Via an Elegant HarmonicNumbers Operational Matrix of Derivatives
• Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs
• Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type
• On the coefficients of differentiated expansions and derivatives of Jacobi polynomials
• A method for high-order multipoint boundary value problems with Birkhoff-type conditions
• A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

This page was built for publication: Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations