Asymptotic Eigenvalue Analysis for a Conformable Fractional Sturm--Liouville Problem
Abstract
This paper is devoted to the study of a Sturm--Liouville problem governed by the conformablefractional derivative of order $\alpha \in (0,1]$.We establish the asymptotic behavior of the corresponding eigenvalues subject to appropriateboundary conditions.Through the construction of suitable fundamental solutions and a detailed analysis of theassociated characteristic equation, explicit asymptotic eigenvalue formulas are obtained.These results elucidate the influence of the conformable fractional operator on the classicalspectral properties and lay a solid analytical foundation for further studies ofconformable fractional Sturm--Liouville theory.
Keywords
Conformable fractional derivative, Sturm--Liouville problem, Fractional eigenvalues, Asymptotic analysis, Fundamental solutions
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