OPERATIONAL MATRICES FOR SOLVING A CLASS OF VARIABLE-ORDER PARTIAL DIFFERENTIAL EQUATIONS

Tingting Zhou, Mahluli Naisbitt Ncube, Saha Salati and Hossein Jafari
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Tingting Zhou: Department of Mathematics, Jilin University, Changchun 130012, P. R. China
Mahluli Naisbitt Ncube: ��Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa
Saha Salati: ��Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran¶Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria, South Africa
Hossein Jafari: ��Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa‡Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran§Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110112, Taiwan

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-9

Abstract: In this paper, we present a numerical technique which is capable of handling variable-order partial differential equations. In this approach, we replace the partial derivatives with operational matrices. We make use of the collocation points to create a system of algebraic equations. The solutions of this system of equations enable us to attain an approximate solution of a variable-order partial differential equation. We demonstrate, with the aid of practical examples, that this method has the ability to deal with complex problems in a fairly straightforward manner and is also highly accurate.

Keywords: Taylor Polynomials; Operational Matrices; Fractional Partial Differential Equations; Variable-Order Partial Differential Equations (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401309

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