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

Mays Basim, Norazak Senu, Zarina Bibi Ibrahim, Ali Ahmadian and Soheil Salahshour
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Mays Basim: Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia
Norazak Senu: Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, Malaysia†Department of Mathematics, Universiti Putra Malaysia, Selangor, Malaysia
Zarina Bibi Ibrahim: ��Department of Mathematics, Universiti Putra Malaysia, Selangor, Malaysia
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
Soheil Salahshour: �Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-13

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: Fractal Differential Equations; Spectral Method; Nonsingular Kernel Derivatives (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400412

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