Representation of Solutions for Sturm-Liouville Eigenvalue Problems With Generalized Fractional Derivative

Abstract

We analyze fractional Sturm-Liouville problems with a new generalized fractional derivative in five different forms. We investigate the representation of solutions by means of rho-Laplace transform for generalized fractional Sturm-Liouville initial value problems. Finally, we examine eigenfunctions and eigenvalues for generalized fractional Sturm-Liouville boundary value problems. All results obtained are compared with simulations in detail under different alpha fractional orders and real rho values. Published under license by AIP Publishing.