Properties of Hadamard Fractional Integral and Its Application

Abstract

We begin by introducing some function spaces Lcp(R+),Xcp(J) made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties of Mellin convolution operators mapping on these spaces, next, we derive some new boundedness and continuity properties of Hadamard integral operators mapping on Xcp(J) and Xp(J). Based on this, we investigate a class of boundary value problems for Hadamard fractional differential equations with the integral boundary conditions and the disturbance parameters, and obtain uniqueness results for positive solutions to the boundary value problem under some weaker conditions.