ON NUMERICAL SOLUTION OF MULTI-TERMS FRACTIONAL DIFFERENTIAL EQUATIONS USING SHIFTED CHEBYSHEV POLYNOMIALS

A. Ali, N.H.M. Ali

IJPAM: Volume 120, No. 1 (2018)

Title

ON NUMERICAL SOLUTION OF MULTI-TERMS
FRACTIONAL DIFFERENTIAL EQUATIONS USING
SHIFTED CHEBYSHEV POLYNOMIALS

Authors

Ajmal Ali

, Norhashidah Hj Mohd. Ali

$^{1,2}$ School of Mathematical Science
University of Science
11800 Penang, MALAYSIA

Abstract

This work provides numerical solution to multi-term differential equation of fractional order by collocation method using the Chebyshev polynomials based functions. The fractional derivative are used in Caputo's sense. The method assumed an approximate solution of the forms of shifted Chebyshev polynomials based functions. The assumed approximate solution is now substitute into the multi-term differential equations of fractional order. After a careful implementation of fractional order differential, we collect the equation at some suitable points and solve it together with boundary conditions to obtain a system of easily solvable linear or nor linear algebraic equations. Numerical examples of multi-order fractional differential equations (MOFDEs) are present to illustrate the method. The results converge to the exact solutions after some iterations and hence it revealed that proposed method is very effective and simple. Thats exposed the validity and applicability of the method.

History

Received: November 30, 2017
Revised: August 21, 2018
Published: August 21, 2018

AMS Classification, Key Words

AMS Subject Classification: 65N14
Key Words and Phrases: Chebyshev polynomials, Caputo's fractional derivative, Multi Order fractional differential equation

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How to Cite?

DOI: 10.12732/ijpam.v120i1.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 1
Pages: 111 - 125

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