Qualitative Investigation of Nonlinear Fractional Coupled Pantograph Impulsive Differential Equations

In this manuscript a qualitative analysis to a nonlinear coupled system of pantograph impulsive fractional differential equations (PIFDEs) is established. By the use of Banach and Krasnoselskii's fixed-point theorems some adequate conditions for the existence and uniqueness of solution to the considered problem are developed. The advantage of using Krasnoselskii's fixed-point theorem is that it uses slight relax compact conditions as compared to other fixed point results. Furthermore, the manuscript is enriched by adding some results about Ulam-Hyers type stability. Finally, with the help of pertinent examples, the obtained theoretical results are justified.