Transmutation of conformable Sturm-Liouville operator with exactly solvable potential

Abstract

In this paper, we proved transformation operator for fractional Sturm-Liouville operator, using conformable derivative approach, 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 alpha = 1 which returns the original problem.