Study of a Snap problem in the Hilfer - Katugampola sense

Abstract

Abstract In our thesis, inspired by the work of Berhail, A., Tabouche, N., Matar, M.M., Samei, M.E., Kaabar, M.K.A., Xiaofeng Wang and Xiao-Guang Yue, which primarily concerns itself with addressing the underlying issues pertaining to the existence, uniqueness, and stability of the solution to the Snap problem in the G-Caputo sense, we consider a con- temporary model of the Snap problem of fractional order in the Hilfer-Katugampola sense with fractional integral conditions ( a novel problem that has yet to be studied ). Firstly, we establish the existence and uniqueness of the solution, which is achieved via the concurrent implementation of both Schauder xed point theorem and Banach contraction principle. Moreover, we explore the stability of the solution to our problem in both Ulam- Hyers and generalized Ulam-Hyers sense. Finally, we provide a numerical simulation in order to understand the theoritical process and illustrate the obtained results.