Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part IIOpen Access

A ROBUST OPERATIONAL MATRIX OF NONSINGULAR DERIVATIVE TO SOLVE FRACTIONAL VARIABLE-ORDER DIFFERENTIAL EQUATIONS

MAYS BASIM

Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia

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NORAZAK SENU

Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia

Department of Mathematics, Universiti Putra Malaysia, Selangor, Malaysia

E-mail Address: norazak@upm.edu.my

Corresponding author.

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ZARINA BIBI IBRAHIM

Department of Mathematics, Universiti Putra Malaysia, Selangor, Malaysia

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ALI AHMADIAN

Institute of IR 4.0, The National University of Malaysia, Selangor, Malaysia

Department of Mathematics, Near East University, Nicosia, TRNC, Mersin 10, Turkey

E-mail Address: ali.ahmadian@ukm.edu.my

Corresponding author.

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, and

SOHEIL SALAHSHOUR

Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

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https://doi.org/10.1142/S0218348X22400412Cited by:5 (Source: Crossref)

Abstract

Currently, a study has come out with a novel class of differential operators using fractional-order and variable-order fractal Atangana–Baleanu derivative, which in turn, became the source of inspiration for new class of differential equations. The aim of this paper is to apply the operation matrix to get numerical solutions to this new class of differential equations and help us to simplify the problem and transform it into a system of an algebraic equation. This method is applied to solve two types, linear and nonlinear of fractal differential equations. Some numerical examples are given to display the simplicity and accuracy of the proposed technique and compare it with the predictor–corrector and mixture two-step Lagrange polynomial and the fundamental theorem of fractional calculus methods.

Keywords:

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Vol. 30, No. 01

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History

Received 20 March 2021

Accepted 25 July 2021

Published: December 28, 2021

Information

This is an Open Access article in the “Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part II”, edited by Yeliz Karaca (University of Massachusetts Medical School, USA), Dumitru Baleanu (Cankaya University, Turkey), Majaz Moonis (University of Massachusetts Medical School, USA), Khan Muhammad (Sejong University, South Korea), Yu-Dong Zhang (University of Leicester, UK) & Osvaldo Gervasi (Perugia University, Italy) 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 ROBUST OPERATIONAL MATRIX OF NONSINGULAR DERIVATIVE TO SOLVE FRACTIONAL VARIABLE-ORDER DIFFERENTIAL EQUATIONS

Abstract

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