Existence and Stability Results for Piecewise Caputo-Fabrizio Fractional Differential Equations with Mixed Delays

In this article, by using the differential Caputo-Fabrizio operator, we suggest a novel family of piecewise differential equations (DEs). The issue under study contains a mixed delay period under the criteria of anti-periodic boundaries. It is possible to utilize the piecewise derivative to describe a variety of complex, multi-step, real-world situations that arise from nature. Using fixed point (FP) techniques, like Banach's FP theorem, Schauder's FP theorem, and Arzela Ascoli's FP theorem, the Hyer-Ulam (HU) stability and the existence theorem conclusions are investigated for the considered problem. Eventually, a supportive example is given to demonstrate the applicability and efficacy of the applied concept.