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Optimal Control of Clarke Subdifferential Type Fractional Differential Inclusion with Non-instantaneous Impulses Driven by Poisson Jumps and Its Topological Properties

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Abstract

This article is devoted to studying the topological structure of a solution set for Clarke subdifferential type fractional non-instantaneous impulsive differential inclusion driven by Poisson jumps. Initially, for proving the solvability result, we use a nonlinear alternative of Leray–Schauder fixed point theorem, Gronwall inequality, stochastic analysis, a measure of noncompactness, and the multivalued analysis. Furthermore, the mild solution set for the proposed problem is demonstrated with nonemptyness, compactness, and, moreover, \(R_\delta \)-set. By employing Balder’s theorem, the existence of optimal control is derived. At last, an application is provided to validate the developed theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, India

    N. Durga

  2. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, 624 302, Tamil Nadu, India

    P. Muthukumar

Authors
  1. N. Durga
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  2. P. Muthukumar
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Correspondence to P. Muthukumar.

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Communicated by Sohrab Effati.

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This work was supported by Council of Scientific and Industrial Research (CSIR), Govt. of India under EMR Project, F.No: 25(0273)/17/EMR-II dated 27-04-2017.

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Durga, N., Muthukumar, P. Optimal Control of Clarke Subdifferential Type Fractional Differential Inclusion with Non-instantaneous Impulses Driven by Poisson Jumps and Its Topological Properties. Bull. Iran. Math. Soc. 47 (Suppl 1), 271–305 (2021). https://doi.org/10.1007/s41980-020-00492-5

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  • DOI: https://doi.org/10.1007/s41980-020-00492-5

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