Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

Advances in Difference Equations

Bessem Samet¹  Mohamed A. Abd El Salam²  Khalid K. Ali²  Emad M. H. Mohamed²  M. S. Osman³  Sunil Kumar⁴ 

[1] Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia;Department of Mathematics, Faculty of Science, Al Azhar University, Cairo, Egypt;Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt;Department of Mathematics, National Institute of Technology, 831014, Jamshedpur, Jharkhand, India;

关键词: Chebyshev collocation method;    Nonlinear fractional integro-differential equations;    Functional argument;    Caputo fractional derivatives;   

DOI  :  10.1186/s13662-020-02951-z

来源: Springer

【 摘 要 】

In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of delay, proportional delay, and advanced non-linear arbitrary order Fredholm–Volterra integro-differential equations. Spectral collocation method is extended to study this problem as a matrix discretization scheme, where the fractional derivatives are characterized in the Caputo sense. The collocation method transforms the given equation and conditions to an algebraic nonlinear system of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. The introduced operational matrix of derivatives includes arbitrary order derivatives and the operational matrix of ordinary derivative as a special case. To the best of authors’ knowledge, there is no other work discussing this point. Numerical test examples are given, and the achieved results show that the recommended method is very effective and convenient.

【 授权许可】

CC BY