On the Boundary Value Problems of Hadamard Fractional Differential EquationswithGeneralized Ulam-HyersStability in BanachSpaces

Abstract

Weshow the mild solutions in Banach space for a first order semi-linear integro-differential equation. We discuss a generalized quantum fractional Sturm-Liouville-Langevin difference problem with terminal boundary conditions. We characterize the relevant results rely on Mönch’s fixed point theorem by terms of Kuratowski measure of non-compactness (MNC) and the Banach contraction principle (BCP). We study the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order.