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Sharp asymptotics in a fractional Sturm-Liouville problem

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Abstract

The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a different route, namely, construction of explicit asymptotic approximations for the solutions. As a study case, we consider a problem with left and right Riemann-Liouville derivatives, for which our analysis yields asymptotically sharp estimates for the sequence of eigenvalues and eigenfunctions.

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Authors and Affiliations

  1. Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel

    Pavel Chigansky

  2. Laboratoire de Statistique et Processus, Le Mans Université, Le Mans, France

    Marina Kleptsyna

Authors
  1. Pavel Chigansky
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  2. Marina Kleptsyna
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Correspondence to Pavel Chigansky.

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Chigansky, P., Kleptsyna, M. Sharp asymptotics in a fractional Sturm-Liouville problem. Fract Calc Appl Anal 24, 715–738 (2021). https://doi.org/10.1515/fca-2021-0031

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