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

In this paper we introduce two integral transforms involving the Legendre function in the kernel (see the operators I0+α,β,μ,v and I−α,β,μ,v. defined below) which generalize the classical Liouville fractional integrals. Then, we study their boundedness as operators mapping the space Lv,r into the spaces Lv−α,r. Moreover, we calculate the Mellin transform of the fractional integrals presented in this paper.