Qualitative Study on Solutions of Piecewise Nonlocal Implicit Fractional Differential Equations

Abstract

In this paper, we investigate new types of nonlocal implicit problems involving piecewise Caputo fractional operators. The existence and uniqueness results are proved by using some fixed point theorems. Furthermore, we present analogous results involving piecewise Caputo-Fabrizio and Atangana–Baleanu fractional operators. The ensuring of the existence of solutions is shown by Ulam-Hyer’s stability. At last, two examples are given to show and approve our outcomes.

Global existence and blow up of solution of wave nonlinear equation with boundary fractional damping and logarithmic source terms

“…Notably, Liquing Lu and Shengjia Li's work [23] specifically delves into this issue. Additionally, various authors, including those referenced as [1,4,5,9], have examined the blow-up problem within the framework of a Lame system. The significance of studying this specific system arises from its widespread applicability in diverse fields, such as potential problems [10].…”