Some properties of generalized fractional integral with Lengendre functions kernels

Abstract

In this paper we introduce two integral transforms involving the Legendre function in the kernel which generalize the classical Liouville fractional integrals. Then, we study their boundedness as operators mapping the space L_{v,r} into the spaces L_{v−α,r}. Moreover, we calculate the Mellin transform of the fractional integrals presented in this paper.