APPLICATION OF HOSOYA POLYNOMIAL TO SOLVE A CLASS OF TIME-FRACTIONAL DIFFUSION EQUATIONS

Hossein Jafari, Roghayeh Moallem Ganji (), Sonali Mandar Narsale, Maluti Kgarose and Nguyen van Thinh
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Hossein Jafari: Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran†Department of Mathematical Sciences, University of South Africa, UNISA0003, Pretoria, South Africa‡Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan
Roghayeh Moallem Ganji: Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
Sonali Mandar Narsale: �Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune 412115, India
Maluti Kgarose: ��Department of Mathematical Sciences, University of South Africa, UNISA0003, Pretoria, South Africa
Nguyen van Thinh: �Department of Civil and Environmental Engineering, Seoul National University, Seoul, South Korea

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-12

Abstract: In this paper, we study time-fractional diffusion equations such as the time-fractional Kolmogorov equations (TF–KEs) and the time-fractional advection–diffusion equations (TF–ADEs) in the Caputo sense. Here, we have developed the operational matrices (OMs) using the Hosoya polynomial (HP) as basis function for OMs to obtain solution of the TF–KEs and the TF–ADEs. The great benefit of this technique is converting the TF–KEs and the TF–ADEs to algebraic equations, which can be simply solved the problem under study. We provide error bound for the approximation of a bivariate function using the HP. Furthermore, comparison of the numerical results obtained using the proposed technique with the exact solution is done. The results prove that the proposed numerical method is most relevant for solving the TF–KEs and the TF–ADEs and accurate.

Keywords: Time-Fractional Kolmogorov Equations; Fractional Advection–Diffusion Equations; Hosoya Polynomial; Operational Matrix (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400595

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