Theory and numerical approaches of high order fractional Sturm-Liouville problems

Authors

TAHEREH HOULARI
MOHAMMAD DEHGHAN
JAFAR BIAZAR
ALIREZA NOURI

DOI

10.3906/mat-1710-103

Abstract

In this paper, fractional Sturm--Liouville problems of high-order are studied. A simple and efficient approach is presented to determine more eigenvalues and eigenfunctions than other approaches. Existence and uniqueness of solutions of a fractional high-order differential equation with initial conditions is addressed as well as the convergence of the proposed approach. This class of eigenvalue problems is important in finding solutions to linear fractional partial differential equations (LFPDE). This method is illustrated by three examples to signify the efficiency and reliability of the proposed numerical approach.

Keywords

High-order fractional Sturm-Liouville problems, eigenvalues, fractional derivative, fixed point theory

First Page

1564

Last Page

1579

Recommended Citation

HOULARI, TAHEREH; DEHGHAN, MOHAMMAD; BIAZAR, JAFAR; and NOURI, ALIREZA (2021) "Theory and numerical approaches of high order fractional Sturm-Liouville problems," Turkish Journal of Mathematics: Vol. 45: No. 4, Article 6. https://doi.org/10.3906/mat-1710-103
Available at: https://journals.tubitak.gov.tr/math/vol45/iss4/6