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Numerical approximation to Prabhakar fractional Sturm–Liouville problem

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Abstract

In this paper, we treat a numerical scheme for the regular fractional Sturm–Liouville problem containing the Prabhakar fractional derivatives with the mixed boundary conditions. We show that the eigenfunctions corresponding to distinct numerical eigenvalues are orthogonal in the Hilbert spaces. The numerical errors and convergence rates are also investigated. Further, we consider a space-fractional diffusion equation and study the associated fractional Sturm–Liouville problem along with the convergence analysis.

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Acknowledgements

The authors would like to thank the referee for the constructive comments which substantially helped improving the quality of paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran

    Mohammad Hossein Derakhshan & Alireza Ansari

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  1. Mohammad Hossein Derakhshan
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  2. Alireza Ansari
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Correspondence to Alireza Ansari.

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Communicated by Vasily E. Tarasov.

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Derakhshan, M.H., Ansari, A. Numerical approximation to Prabhakar fractional Sturm–Liouville problem. Comp. Appl. Math. 38, 71 (2019). https://doi.org/10.1007/s40314-019-0826-4

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  • DOI: https://doi.org/10.1007/s40314-019-0826-4

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