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Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by fBm with Noncompact Semigroup via Mönch Fixed Point

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Abstract

The aim of this work is to study the mild solutions for a class of impulsive neutral stochastic functional integrodifferential equations driven by fractional Brownian motion using noncompact semigroup in a Hilbert space. We assume that the linear part has a resolvent operator not necessarily compact but the operator norm is continuous. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Mönch fixed point theorem. Furthermore, under some suitable assumptions, the considered system’s trajectory (T-) controllability is established using generalized Gronwall’s inequality. An example is delivered to illustrate the obtained theoretical results. Finally, real life fermentation example is discussed to supporting the proposed system.

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Authors and Affiliations

  1. Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 014, India

    Ramkumar Kasinathan & Ravikumar Kasinathan

  2. Department of Applied Mathematics, Virginia Military Institute, Lexington, VA, 24450, USA

    Dimplekumar Chalishajar

  3. Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, 641 202, India

    Varshini Sandrasekaran

  4. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

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  1. Ramkumar Kasinathan
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  2. Ravikumar Kasinathan
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  3. Dimplekumar Chalishajar
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  4. Varshini Sandrasekaran
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  5. Dumitru Baleanu
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Contributions

All authors contributed equally in writing this article. We all investigated the problem, proposed regularity assumptions, proved the results, and gave an illustrative example. All authors read and approved the final manuscript.

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Correspondence to Dimplekumar Chalishajar.

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Kasinathan, R., Kasinathan, R., Chalishajar, D. et al. Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by fBm with Noncompact Semigroup via Mönch Fixed Point. Qual. Theory Dyn. Syst. 23, 72 (2024). https://doi.org/10.1007/s12346-023-00917-6

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