Stochastic controllability for a non-autonomous fractional neutral differential equation with infinite delay in abstract space

2024/03/10 by Areefa Khatoon, Khatoon, Areefa, Abdur Raheem +3
Engineering · Mathematics · #26A33 #34K05 #34K35 #47H08 #93B05 #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2403.08825

openalex publication_date 2024/03/10 · openalex created_date 2024/03/16 · openalex updated_date 2026/07/28

Abstract

This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and stochastic analysis techniques have been implemented to achieve the main result. We prove the existence of mild solution and controllability of the system by using the theory of measure of non-compactness, fixed point theorems, and k-set contractive mapping. An example is given to demonstrate the effectiveness of the abstract result.

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