Analysis of nonlinear implicit Caputo-Katugampola fractional differential equation with quasi-periodic boundary condition

Abstract

In this paper, we discuss a class of implicit fractional differential equation with quasi-periodic boundary condition involving Caputo-Katugampola fractional derivative. Based on different parameter values, we utilize Mawhin’s continuation theorem, Schaefer’s fixed point theorem, and Banach’s contraction mapping principle, respectively, to provide the existence, uniqueness, and Ulam-type stability of the solutions to the considered problem, and provide several examples to illustrate the main results.