On finite fractional Sturm–Liouville transforms

Abstract

In this article, we introduce the finite fractional Sturm–Liouville transforms for the four classes of fractional operators involving the left-sided and right-sided Riemann–Liouville, Caputo and Weyl fractional derivatives. Moreover, the inversion formulas are drawn and the formal and numerical solutions of some partial fractional differential equations are obtained using the finite fractional Legendre, Hankel and Fourier transforms.

Keywords:

• Sturm–Liouville problem
• finite transform
• fractional derivative
• partial fractional differential equation

Mathematics Subject Classification:

• 26A33
• 34B24

Acknowledgments

The author wishes to thank the referees for their constructive comments and suggestions.