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<p>This paper explores Sobolev-type Atangana–Baleanu fractional stochastic differential inclusions driven by fractional Brownian motion, incorporating Clarke sub-differentials, Poisson jumps, and nonlocal conditions. Through the use of fractional calculus (<Emphasis FontCategory="NonProportional">FC</Emphasis>), stochastic analysis (<Emphasis FontCategory="NonProportional">SA</Emphasis>), and fixed-point techniques, the authors derive sufficient conditions for nonlocal controllability. The analysis leverages the properties of Clarke sub-differentials and non-smooth analysis. An illustrative example is provided to highlight the practical application and significance of the findings.</p>

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The effects of Clarke sub-differential and Poisson jumps on nonlocal controllability of Sobolev-type fractional stochastic differential inclusions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月7日

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  • Wael W. Mohammed,
  • Hamdy M. Ahmed,
  • Homan Emadifar,
  • Karim K. Ahmed,
  • A. M. Sayed Ahmed

摘要

This paper explores Sobolev-type Atangana–Baleanu fractional stochastic differential inclusions driven by fractional Brownian motion, incorporating Clarke sub-differentials, Poisson jumps, and nonlocal conditions. Through the use of fractional calculus (FC), stochastic analysis (SA), and fixed-point techniques, the authors derive sufficient conditions for nonlocal controllability. The analysis leverages the properties of Clarke sub-differentials and non-smooth analysis. An illustrative example is provided to highlight the practical application and significance of the findings.