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research-article

New Operational Matrix for Solving Multi-Term Variable Order Fractional Differential Equations

[+] Author and Article Information
A. M. Nagy

Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
abdelhameed_nagy@yahoo.com

Nasser Sweilam

Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
nsweilam@sci.cu.edu.eg

Adel A. El-Sayed

Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt
aaa18@fayoum.edu.eg

1Corresponding author.

ASME doi:10.1115/1.4037922 History: Received September 22, 2016; Revised September 07, 2017

Abstract

The multi-term fractional variable-order differential equation has a massive application in physics and engineering problems. Therefore, a numerical method is presented to solve a class of variable order fractional differential equations (FDEs) based on an operational matrix of shifted Chebyshev polynomials of the fourth kind. Utilizing the constructed operational matrix, the fundamental problem is reduced to an algebraic system of equations which can be solved numerically. Error estimate of the proposed method is studied. Finally, the accuracy, applicability, and validity of the suggested method are illustrated through several examples.

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