Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses

Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses

This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we t...

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Bibliographic Details
Main Authors: Hasanen A. Hammad, Manuel De la Sen
Format: Article
Language:English
Published: Elsevier 2025-01-01
Series:Alexandria Engineering Journal
Subjects:
Bohnenblust–Karlin FP approaches
Stochastic systems
Approximate controllability
Fractional derivatives
Nonlinear equations
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016824011736
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Summary:This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we transform the system into an equivalent fixed-point (FP) problem through an integral operator. Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. By assuming ACA of the corresponding linear system, we derive sufficient conditions for the ACA of the nonlinear stochastic impulsive control system. Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). The theoretical findings are illustrated through a concrete example.
ISSN:1110-0168

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