Tripled Fixed Points and Existence Study to a Tripled Impulsive Fractional Differential System via Measures of Noncompactness

Sina Etemad,Maria Alessandra Ragusa,Mohammed M Matar,Shahram Rezapour

doi:10.3390/math10010025

Abstract

In this paper, a tripled fractional differential system is introduced as three associated impulsive equations. The existence investigation of the solution is based on contraction principle and measures of noncompactness in terms of tripled fixed point and modulus of continuity. Our results are valid for both Kuratowski and Hausdorff measures of noncompactness. As an application, we apply the obtained results to a control problem.

Highlights

Fractional differential equations are considered as the most appropriate models for many applicable phenomena
The investigations of existence problems of fractional differential equations have diverse topics ranging from the shape of initial and boundary conditions including impulsive conditions, throughout various types of the used fractional derivatives, and reaching to different forms fixed point theorems
We designed a tripled system consisting of impulsive fractional equations involving the generalized boundary conditions with some given operators

Summary

Introduction

Fractional differential equations are considered as the most appropriate models for many applicable phenomena (see in [1,2] and references therein). Tripled Fixed Points and Existence Study to a Tripled Impulsive Fractional Differential System via Measures of Noncompactness. The fixed point theorems are essential resources for solving many existence problems of solutions of differential and integral equations.

Results

Conclusion