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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, 632 014, India

    C. Dineshkumar, R. Udhayakumar & V. Vijayakumar

  2. Department of Applied Science, Rajkiya Engineering College Kannauj, Kannauj, 209732, India

    Anurag Shukla

  3. Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, 11991, Wadi Aldawaser, Saudi Arabia

    Kottakkaran Sooppy Nisar

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  1. C. Dineshkumar
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  2. R. Udhayakumar
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Dineshkumar, C., Udhayakumar, R., Vijayakumar, V. et al. Discussion on the Approximate Controllability of Nonlocal Fractional Derivative by Mittag-Leffler Kernel to Stochastic Differential Systems. Qual. Theory Dyn. Syst. 22, 27 (2023). https://doi.org/10.1007/s12346-022-00725-4

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