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

2021/12/14 by Lavina Sahijwani, Sahijwani, Lavina, N. Sukavanam +3
Engineering · Mathematics · #26A33 #34G20 #34K37 #93B05 #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.07643

openalex publication_date 2021/12/14 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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.

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