Lyapunov stability and solvability of nonlocal fractional differential equations with generalized katugampola derivative

This paper investigates a class of fractional differential equations (FDEs) that involve the generalized Katugampola fractional derivative (FD) subject to nonlocal boundary conditions. By transforming the considered boundary value problems (BVPs) into equivalent integral equations, we establish several results concerning the existence and uniqueness of solutions. The analysis is carried out using classical fixed point (FP) techniques, including the Banach contraction principle(BC), as well as Schaefer's FP theorems under appropriate assumptions. In addition, we examine the Lyapunov stability of nontrivial solutions and derive sufficient conditions to ensure asymptotic stability. The obtained results extend and complement the existing contributions in the literature on fractional BVPs with nonlocal conditions. Finally, illustrative examples are provided to demonstrate the applicability of the theoretical findings.