Discussion on the Approximate Controllability of Nonlocal Fractional Derivative by Mittag-Leffler Kernel to Stochastic Differential Systems

• C. Dineshkumar ^[2] ; R. Udhayakumar ^[2] ; V. Vijayakumar ^[2] ; Anurag Shukla ^[3] ; Kottakkaran Sooppy Nisar ^[1]
  1. [1] Prince Sattam Bin Abdulaziz University

     Prince Sattam Bin Abdulaziz University

     Arabia Saudí

     
  2. [2] Vellore Institute of Technology
  3. [3] Rajkiya Engineering College Kannauj

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
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• Resumen

  • This article is primarily targeting the approximate controllability of nonlocal Atangana–Baleanu fractional derivative by Mittag-Leffler kernel to stochastic differential systems. In particular, we obtain a new set of sufficient conditions for the approximate controllability of nonlinear Atangana–Baleanu fractional stochastic differential inclusions under the assumption that the corresponding linear system is approximately controllable. In addition, we establish the approximate controllability results for the Atangana–Baleanu fractional stochastic control system with infinite delay. The results are obtained with the help of the fixed-point theorem for multivalued operators and fractional calculus. At last, an example is included to show the applicability of our results.