TRANSMUTATION OF FRACTIONAL STURM-LIOUVILLE OPERATOR WITH EXACTLY SOLVABLE POTENTIAL

Abstract

In this paper, we proved transformation operator for fractional Sturm-Liouville operator which is different from classical Sturm-Liouville operator. Especially, we obtained a Hyperbolic partial differential equation and some suitable conditions for nucleus function K(x, t). Finally, we obtained a Fredholm integral equation. The proof is validated by taking α = 1 which returns the original problem.