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Direct and inverse problems of fractional Sturm–Liouville equation

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Abstract

In this paper we define a fractional Sturm–Liouville problem (FSLP) on [0, 1] subject to dirichlet boundary condition. First we discretize FSLP to obtain the corresponding matrix eigenvalue problem (MEP) of finite order N. In direct problem we give an efficient numerical algorithm to make good approximations for eigenvalues of FSLP by adding a correction term to eigenvalues of MEP. For inverse problem, using the idea of correction technique, we propose an algorithm for recovering the symmetric potential function using one given spectrum. Finally, we give some numerical examples to show the efficiency of the proposed algorithm.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

    Zahra Kavousi Kalashmi, Hanif Mirzaei & Kazem Ghanbari

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  1. Zahra Kavousi Kalashmi
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  2. Hanif Mirzaei
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  3. Kazem Ghanbari
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All authors contributed equally in the preparation of the manuscript. H. Mirzaei wrote the main manuscript text. All authors reviewed the final version of the manuscript.

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Correspondence to Hanif Mirzaei.

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Kalashmi, Z.K., Mirzaei, H. & Ghanbari, K. Direct and inverse problems of fractional Sturm–Liouville equation. Optim Eng (2024). https://doi.org/10.1007/s11081-024-09881-9

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