On finite fractional Sturm-Liouville transforms

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.