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An Operational Matrix Technique Based on Chebyshev Polynomials for Solving Mixed Volterra-Fredholm Delay Integro-Differential Equations of Variable-Order

Authors :
R. Raslan, Kamal
K. Ali, Khalid
M. H. Mohamed, Emad
A. Younis, Jihad
A. Abd El salam, Mohamed
Source :
Journal of Function Spaces; 2022, Vol. 2022 Issue: 1
Publication Year :
2022

Abstract

In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) of variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) of the first kind with the spectral collocation method. The proposed VO-LFDIDEs have multiterms of integer, fractional-order derivatives for delayed or nondelayed and mixed Volterra-Fredholm integral terms. The introduced model is a more general form of linear fractional VO pantograph, neutral, and mixed Fredholm–Volterra integro-differential equations with delay arguments. Caputo’s VO fractional derivative operator is used to generate the matrices of the derivative. Operational matrices are presented for all terms. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. Also, some examples are included to improve the validity and applicability of the techniques. Finally, comparisons between the proposed method and other methods were used to solve this kind of equation.

Details

Language :
English
ISSN :
23148896 and 23148888
Volume :
2022
Issue :
1
Database :
Supplemental Index
Journal :
Journal of Function Spaces
Publication Type :
Periodical
Accession number :
ejs59407380
Full Text :
https://doi.org/10.1155/2022/6203440