Abstract
In this paper, we consider a regular Fractional Sturm–Liouville Problem (FSLP) of order μ (0 < μ < 1). We approximate the eigenvalues and eigenfunctions of the problem using a fractional variational approach. Recently, Klimek et al. [16] presented the variational approach for FSLPs defined in terms of Caputo derivatives and obtained eigenvalues, eigenfunctions for a special range of fractional order 1/2 < μ < 1. Here, we extend the variational approach for the FSLPs and approximate the eigenvalues and eigenfunctions of the FSLP for fractional-order μ (0 < μ < 1). We also prove that the FSLP has countably infinite eigenvalues and corresponding eigenfunctions.
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Pandey, P.K., Pandey, R.K. & Agrawal, O.P. Variational Approximation for Fractional Sturm–Liouville Problem. Fract Calc Appl Anal 23, 861–874 (2020). https://doi.org/10.1515/fca-2020-0043
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DOI: https://doi.org/10.1515/fca-2020-0043