ArticleOpen Access

A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS

ADNAN KHAN

Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan

E-mail Address: adnankhan.gogara@gmail.com

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KAMAL SHAH

Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan

E-mail Address: kamalshah408@gmail.com

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MUHAMMAD ARFAN

Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan

E-mail Address: arfan_uom@yahoo.com

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THABET ABDELJAWAD

Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia

Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

E-mail Address: tabdeljawad@psu.edu.sa

Corresponding author.

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, and

FAHD JARAD

Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey

E-mail Address: fahd@cankaya.edu.re

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https://doi.org/10.1142/S0218348X20400460Cited by:1 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

In this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.

Keywords:

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Vol. 28, No. 08

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History

Received 26 December 2019

Accepted 28 February 2020

Published: July 6, 2020

Information

This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS

Abstract

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