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arXiv · 1712.09894

Fractional Sturm-Liouville eigenvalue problems, II

Mohammad Dehghan·Angelo B. Mingarelli
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Abstract

We continue the study of a non self-adjoint fractional three-term Sturm-Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left-Riemann-Liouville fractional integral under {\it Dirichlet type} boundary conditions. We study the existence and asymptotic behavior of the real eigenvalues and show that for certain values of the fractional differentiation parameter $\alpha$, $0<\alpha<1$, there is a finite set of real eigenvalues and that, for $\alpha$ near $1/2$, there may be none at all. As $\alpha \to 1^-$ we show that their number becomes infinite and that the problem then approaches a standard Dirichlet Sturm-Liouville problem with the composition of the operators becoming the operator of second order differentiation.

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Mohammad Dehghan, Angelo B. Mingarelli. 2017-12-28. Fractional Sturm-Liouville eigenvalue problems, II. https://doi.org/10.3390/fractalfract6090487

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