A study on the exact controllability of stochastic impulsive fractional integro-differential evolution equations under nonlocal conditions employing resolvent operator techniques

Hasanen A. Hammad and Doha A. Kattan

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: This manuscript investigates the exact controllability of a class of stochastic impulsive fractional integro-differential evolution equations with nonlocal conditions and history-dependent operators in a Hilbert space framework, without imposing the compactness of the semigroup generated by the linear part, thereby significantly enlarging the class of admissible infinite-dimensional systems. The model incorporates fractional dynamics, stochastic perturbations, impulsive effects, and memory terms under suitable mild assumptions, providing a realistic and comprehensive description of complex evolution processes. The main results are derived by combining Mönch’s fixed-point theorem with the measure of noncompactness and stochastic analysis techniques, which effectively overcome difficulties caused by noncompactness and hereditary effects. Moreover, suitable control functions are constructed to ensure exact controllability over a finite time interval. The main advantage of this work lies in relaxing restrictive compactness assumptions while simultaneously handling stochasticity, impulses, and memory effects within a unified framework. Finally, illustrative examples are provided to demonstrate the applicability and effectiveness of the obtained results and to highlight their improvement over existing literature.

Keywords: Fractional derivative; Integro-differential evolution equation; Approximate controllability; History-dependent operator; Mönch’s fixed point theorem (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926007952

DOI: 10.1016/j.chaos.2026.118654

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