Properties of Hadamard Fractional Integral and Its Application
Weiwei Liu, Lishan Liu
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.
Topics & Concepts
Hadamard transformMathematicsUniquenessConvolution (computer science)Mathematical analysisBoundary value problemFractional calculusFunction (biology)Integrable systemPure mathematicsBoundary (topology)Class (philosophy)Artificial neural networkBiologyEvolutionary biologyComputer scienceArtificial intelligenceMachine learningNonlinear Differential Equations AnalysisFixed Point Theorems AnalysisDifferential Equations and Boundary Problems