Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis

TL;DR

This paper investigates the existence and controllability of non-linear fractional differential systems with non-instantaneous impulses using Riemann-Liouville derivatives, providing theoretical results and illustrative examples.

Contribution

It introduces a new framework for analyzing controllability of fractional impulsive systems with Riemann-Liouville derivatives, including existence proofs and correction of previous examples.

Findings

Existence of mild solutions established via Banach's fixed point theorem.

Approximate controllability results derived using fractional semigroup theory.

Examples demonstrate the applicability and correctness of the proposed methods.

Abstract

The article is dedicated towards the study of fractional order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions in Banach spaces. First, mild solution of the system is constructed and subsequently its existence is proven using Banach's fixed point theorem. Then, results of approximate controllability are established using concept of fractional semigroup and an iterative technique. Suitable examples are given in the end supporting the methodology along with pointing out correction in examples presented in previous articles.