TY - JOUR
A2 - Elsadany, Abdelalim
AU - Al-Refai, Mohammed
AU - Abdeljawad, Thabet
PY - 2017
DA - 2017/09/14
TI - Fundamental Results of Conformable Sturm-Liouville Eigenvalue Problems
SP - 3720471
VL - 2017
AB - We suggest a regular fractional generalization of the well-known Sturm-Liouville eigenvalue problems. The suggested model consists of a fractional generalization of the Sturm-Liouville operator using conformable derivative and with natural boundary conditions on bounded domains. We establish fundamental results of the suggested model. We prove that the eigenvalues are real and simple and the eigenfunctions corresponding to distinct eigenvalues are orthogonal and we establish a fractional Rayleigh Quotient result that can be used to estimate the first eigenvalue. Despite the fact that the properties of the fractional Sturm-Liouville problem with conformable derivative are very similar to the ones with the classical derivative, we find that the fractional problem does not display an infinite number of eigenfunctions for arbitrary boundary conditions. This interesting result will lead to studying the problem of completeness of eigenfunctions for fractional systems.
SN - 1076-2787
UR - https://doi.org/10.1155/2017/3720471
DO - 10.1155/2017/3720471
JF - Complexity
PB - Hindawi
KW -
ER -