Some properties of generalized fractional integral with Lengendre functions kernel’s

Abstract

Abstract. In this paper we introduce two integral transforms involving the Legendre function in the kernel (see the operators I α,β ,μ,ν 0 + and I α,β ,μ,ν − defined below) 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.