A NUMERICAL SCHEME FOR A CLASS OF NONLINEAR MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATIONS

Hossein Jafari, Saha Salati, Mashallah Matinfar and Nguyen van Thinh
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Hossein Jafari: Institute of Research and Development, Duy Tan University, Da Nang, Vietnam†School of Engineering & Technology, Duy Tan University, Da Nang, Vietnam‡Department of Mathematical Sciences, University of South Africa UNISA0003, South Africa§Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110112, Taiwan
Saha Salati: �Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
Mashallah Matinfar: �Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
Nguyen van Thinh: ��Department of Civil and Environmental Engineering, Seoul National University, Seoul, South Korea

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-12

Abstract: In this paper, we obtain a numerical solution for a class of nonlinear multi-order fractional differential equations by using operational matrices. The fractional derivative is the Caputo derivative and operational matrices is calculated by using the Hosoya polynomials of simple paths. By using the operational matrices, we reduce the governing problem to a system of nonlinear algebraic equations. We present a few numerical examples which shown the performance and precision of the proposed technique.

Keywords: Operational Matrices; Hosoya Polynomials; Caputo Derivative; Numerical Solution; Nonlinear Multi-order Fractional Differential Equations (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401322

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