(<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces

Abstract

The paper focuses on exploring the existence and uniqueness of a specific solution to a class of Caputo impulsive fractional differential equations with boundary value conditions on Banach space, referred to as (ω,ρ)-BVP solution. The proof of the main results of this study involves the application of the Banach contraction mapping principle and Schaefer’s fixed point theorem. Furthermore, we provide the necessary conditions for the convexity of the set of solutions of the analyzed impulsive fractional differential boundary value problem. To enhance the comprehension and practical application of our findings, we conclude the paper by presenting two illustrative examples that demonstrate the applicability of the obtained results.

Keywords

• (<i>ω</i>,<i>ρ</i>)-BVP solutions
• boundary value problem
• impulsive fractional equations