Numerical study for a class of time fractional diffusion equations using operational matrices based on Hosoya polynomial

Ping Zhou; Hossein Jafari; Roghayeh M. Ganji; Sonali M. Narsale; Ping Zhou; Hossein Jafari; Roghayeh M. Ganji; Sonali M. Narsale

doi:10.3934/era.2023231

Electronic Research Archive

2023, Volume 31, Issue 8: 4530-4548. doi: 10.3934/era.2023231

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Numerical study for a class of time fractional diffusion equations using operational matrices based on Hosoya polynomial

1.
School of Artificial Intelligence, Wenshan University, Wenshan, China
2.
Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
3.
Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5.
Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Pune, India

Received: 04 April 2023 Revised: 18 May 2023 Accepted: 29 May 2023 Published: 19 June 2023

In this paper, we develop a numerical method by using operational matrices based on Hosoya polynomials of simple paths to find the approximate solution of diffusion equations of fractional order with respect to time. This method is applied to certain diffusion equations like time fractional advection-diffusion equations and time fractional Kolmogorov equations. Here we use the Atangana-Baleanu fractional derivative. With the help of this approach we convert these equations to a set of algebraic equations, which is easier to be solved. Also, the error bound is provided. The obtained numerical solutions using the presented method are compared with the exact solutions. The numerical results show that the suggested method is convenient and accurate.
- Hosoya polynomial,
- fractional advection-diffusion equations,
- time-fractional Kolmogorov equations,
- operational matrix,
- numerical results
Citation: Ping Zhou, Hossein Jafari, Roghayeh M. Ganji, Sonali M. Narsale. Numerical study for a class of time fractional diffusion equations using operational matrices based on Hosoya polynomial[J]. Electronic Research Archive, 2023, 31(8): 4530-4548. doi: 10.3934/era.2023231

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Abstract

In this paper, we develop a numerical method by using operational matrices based on Hosoya polynomials of simple paths to find the approximate solution of diffusion equations of fractional order with respect to time. This method is applied to certain diffusion equations like time fractional advection-diffusion equations and time fractional Kolmogorov equations. Here we use the Atangana-Baleanu fractional derivative. With the help of this approach we convert these equations to a set of algebraic equations, which is easier to be solved. Also, the error bound is provided. The obtained numerical solutions using the presented method are compared with the exact solutions. The numerical results show that the suggested method is convenient and accurate.

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