HILFER FRACTIONAL SPECTRAL PROBLEM VIA BESSEL OPERATOR - Panakhov, Etibar; Ercan, Ahu; Bas, Erdal; Ozarslan, Ramazan (Inst Applied Mathematics, 2019)
In this paper, we deal with a modified fractional Hilfer Sturm-Liouville operator for Bessel potential and we show the self-adjointness of the operator, orthogonality of distinct eigenfunctions and reality of eigenvalues. Also, we obtain an integral representation of solution and we give a numerical method for obtaining numerical results by changing alpha, beta values illustrated by graphics.
Keywords: Hilfer; Bessel; spectral theory; fractional; Sturm-Liouville