Numerical Analysis and Applicable Mathematics
Title
A Numerical Technique for Solving Variable Order Fractional Differential-Integral Equations based on Shifted Fractional Jacobi–Gauss Polynomials
Authors
Elham Rezazadeha and Mohammad Hossein Derakhshan*b
aDepartment of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
bDepartment of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran.
*Corresponding author E-mail address: m.h.derakhshan.20@gmail.com (Derakhshan M. H.)
Article History
Publication details: Received: 09th July 2021; Revised: 05th July 2022; Accepted: 12th July 2022; Published: 14th July 2022
Cite this article
Rezazadeh E.; Derakhshan M. H. A Numerical Technique for Solving Variable Order Fractional Differential-Integral Equations based on Shifted Fractional Jacobi–Gauss Polynomials. Numer. Anal. Appl. Math., 2022, 3(6), 1-9.
Abstract
In this manuscript, we display the following coupled differential-integral equations including the Caputo fractional operator of variable-orders: CaputoDe1(x)[p1(x)]+ p1’(x)+ p1(v)dv=q1(x), CaputoDe2(x)[p2(x)]+ p2’(x)+ p2(v)dv=q2(x), where q1(x), q2(x) are considered the linear and nonlinear functions and 0i(x)≤1,i=1,2. To solve numerically these equations by a numerical method based on the shifted Jacobi-Gauss collocation scheme is used. Using this numerical method a system of algebraic equations is constructed. We solve this system with a recursive method in the nonlinear case and we solve it in linear case with algebraic formulas. Finally, for the high performance of the suggested method three Examples are illustrated.
Keywords
Coupled differential-integral equation; Caputo fractional operator; Shifted fractional Jacobi collocation method; Variable-order
