Authors: TAHEREH HOULARI, MOHAMMAD DEHGHAN, JAFAR BIAZAR, ALIREZA NOURI
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
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