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Research Papers

# New Operational Matrix for Solving Multiterm Variable Order Fractional Differential Equations

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

Department of Mathematics,
Faculty of Science,
Benha University,
Benha 13518, Egypt
e-mail: abdelhameed_nagy@yahoo.com

N. H. Sweilam

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

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

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 22, 2016; final manuscript received September 7, 2017; published online October 9, 2017. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 13(1), 011001 (Oct 09, 2017) (7 pages) Paper No: CND-16-1450; doi: 10.1115/1.4037922 History: Received September 22, 2016; Revised September 07, 2017

## Abstract

The multiterm 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. The 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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