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<p>This paper investigates the controllability of a Hilfer fractional stochastic impulsive differential system with infinite delay. The problem is motivated by the need to model and control complex real-world processes that simultaneously exhibit randomness, long-term memory effects, and abrupt impulsive changes. To analyze this class of systems, we employ a mathematical framework that integrates fractional calculus, semigroup theory, measures of noncompactness, impulsive differential equations, stochastic analysis, and fixed point methods. By constructing an appropriate solution operator and applying the Mönch’s fixed point theorem together with fractional integration techniques, we establish new sufficient conditions that guarantee the controllability of the system. These results extend existing controllability theory for fractional and stochastic systems to a more general Hilfer setting that incorporates both impulses and infinite delay. The applicability of the theoretical results is demonstrated through three examples: an abstract system defined on a spatial domain, a population dynamics model, and a viscoelastic system, illustrating both the generality and practical relevance of the proposed approach.</p>

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A measure of noncompactness approach for controllability of Hilfer fractional stochastic impulsive systems

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Radha Madhuri Indukuri,
  • Balarama Krishna Chebolu,
  • Kavitha Krishnan,
  • Sobhanbabu Yendamuri

摘要

This paper investigates the controllability of a Hilfer fractional stochastic impulsive differential system with infinite delay. The problem is motivated by the need to model and control complex real-world processes that simultaneously exhibit randomness, long-term memory effects, and abrupt impulsive changes. To analyze this class of systems, we employ a mathematical framework that integrates fractional calculus, semigroup theory, measures of noncompactness, impulsive differential equations, stochastic analysis, and fixed point methods. By constructing an appropriate solution operator and applying the Mönch’s fixed point theorem together with fractional integration techniques, we establish new sufficient conditions that guarantee the controllability of the system. These results extend existing controllability theory for fractional and stochastic systems to a more general Hilfer setting that incorporates both impulses and infinite delay. The applicability of the theoretical results is demonstrated through three examples: an abstract system defined on a spatial domain, a population dynamics model, and a viscoelastic system, illustrating both the generality and practical relevance of the proposed approach.