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A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem
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Orientador(es)
Resumo(s)
In this work, we consider the n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.
Descrição
Palavras-chave
Fractional derivatives Fractional Sturm-Liouville problem Fractional variational calculus Eigenvalue problem Eigenfunctions Fractional Clifford analysis
Contexto Educativo
Citação
Ferreira, M., Manuela Rodrigues, M. & Vieira, N. (2021). A fractional analysis in higher dimensions for the Sturm-Liouville problem. Fractional Calculus and Applied Analysis, 24(2), 585-620. https://doi.org/10.1515/fca-2021-0026
Editora
De Gruyter