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Numerical solution of the diffusion problem of distributed order based on the Sinc-collocation method

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Abstract

A numerical method for the diffusion problem with the fractional derivative of distributed order arising in modeling real life phenomena is investigated. The approximation is based on the Sinc-collocation method. We proposed the Sinc-collocation method in both spatial and temporal discretizations of the problem. The fractional derivatives in this article are of the Caputo type. Also, we proved the convergence of the introduced method and an error estimate for it. We have shown the efficiency of the introduced method with the help of several examples. The obtained numerical results confirm the presented convergence analysis.

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Authors and Affiliations

  1. Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran

    Sh. Taherkhani, I. Najafi Khalilsaraye & B. Ghayebi

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  1. Sh. Taherkhani
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  2. I. Najafi Khalilsaraye
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  3. B. Ghayebi
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All authors contributed to the study’s conception and design. The first draft of the manuscript was written by “Sh. Taherkhani” and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to I. Najafi Khalilsaraye.

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Taherkhani, S., Khalilsaraye, I.N. & Ghayebi, B. Numerical solution of the diffusion problem of distributed order based on the Sinc-collocation method. Math Sci 17, 133–144 (2023). https://doi.org/10.1007/s40096-021-00447-9

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  • DOI: https://doi.org/10.1007/s40096-021-00447-9

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