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

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 advectio...

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Bibliographic Details
Published in:Electronic research archive 2023-01, Vol.31 (8), p.4530-4548
Main Authors: Zhou, Ping, Jafari, Hossein, Ganji, Roghayeh M., Narsale, Sonali M.
Format: Article
Language:English
Subjects:
fractional advection-diffusion equations
hosoya polynomial
numerical results
operational matrix
time-fractional kolmogorov equations
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Summary: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.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2023231