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The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential

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  • Upadhyay, Anjali
  • Kumar, Surendra

Abstract

This study explores a new class of stochastic multi-term fractional differential inclusions with the Clarke subdifferential involving the Rosenblatt process. The presence and uniqueness of a solution are determined by the successive approximation approach in combination with the stochastic analysis methodology and the resolvent operators. Furthermore, new sufficient conditions are given to ensure the exponential decay of the mild solution without Lipschitz conditions on non-linear terms. We have also provided an example to validate the obtained results.

Suggested Citation

  • Upadhyay, Anjali & Kumar, Surendra, 2023. "The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923001030
    DOI: 10.1016/j.chaos.2023.113202
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    References listed on IDEAS

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    1. Maejima, Makoto & Tudor, Ciprian A., 2013. "On the distribution of the Rosenblatt process," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1490-1495.
    2. Durga, N. & Muthukumar, P., 2019. "Existence and exponential behavior of multi-valued nonlinear fractional stochastic integro-differential equations with Poisson jumps of Clarke’s subdifferential type," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 347-359.
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    5. N. N. Leonenko & V. V. Anh, 2001. "Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long-range dependence," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-20, January.
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