On the generalized fractional snap boundary problems via G-Caputo operators: existence and stability analysis

Abstract

Abstract This research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the G $\mathbb{G}$ -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional G $\mathbb{G}$ -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders.

Keywords

• Fixed-point
• Generalized fractional operators
• Snap equation
• Special operators