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Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations

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Abstract

This article investigates the analytical and numerical solutions of a class of non-autonomous time-fractional integro-partial differential initial-boundary-value problems (IBVPs) with fractional derivative of Caputo-type. The existence and uniqueness of the analytical solution of the IBVP are established by using the Sumudu decomposition method and the maximum-minimum principle, respectively. To obtain the numerical solution, first, we semi-discretize the IBVP by discretizing the time fractional derivative by using the L1-scheme and the integral term by using the trapezoidal rule on a graded mesh, and then we approximate the spatial derivatives by using the cubic spline method over a uniform mesh. The stability and convergence analysis of the numerical method are established. The performance of the proposed technique is validated through numerical experiments, and the results are compared with the method presented in Santra and Mohapatra (J. Comput. Appl Math. 400, 113746, 13, 2022).

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors wish to acknowledge the referee for his/her valuable comments and suggestions, which helped to improve the article. Furthermore, the first author would like to acknowledge the fellowship and amenities support provided by IIT Guwahati in his research.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Sandip Maji & Srinivasan Natesan

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  1. Sandip Maji
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  2. Srinivasan Natesan
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Contributions

S.N. provided the methodology along with the model problem and re-editing and correcting the manuscript. S.M. implemented the scheme and obtained the error analysis and the numerical experiments and writing the manuscript.

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Correspondence to Srinivasan Natesan.

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Maji, S., Natesan, S. Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations. Numer Algor 94, 229–256 (2023). https://doi.org/10.1007/s11075-023-01498-w

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  • DOI: https://doi.org/10.1007/s11075-023-01498-w

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