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Ulam–Hyers–Rassias stability of Hilfer fractional stochastic impulsive differential equations with non-local condition via Time-changed Brownian motion followed by the currency options pricing model

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  • Chalishajar, Dimplekumar
  • Kasinathan, Dhanalakshmi
  • Kasinathan, Ravikumar
  • Kasinathan, Ramkumar

Abstract

In this paper, a new solution representation and Ulam-Hyer’s Rassias stability of Hilfer fractional stochastic impulsive differential systems (HFSIDEs) with non-local condition via Time-changed fractional Brownian motion (TCFBM) is studied. The wellposedness of solutions are proved in the finite-dimensional space by using fixed point theorem (FPT). Finally, to account for the long-memory property of the spot exchange rate, we offer a novel framework for pricing currency options in line with the TCFBM model.

Suggested Citation

  • Chalishajar, Dimplekumar & Kasinathan, Dhanalakshmi & Kasinathan, Ravikumar & Kasinathan, Ramkumar, 2025. "Ulam–Hyers–Rassias stability of Hilfer fractional stochastic impulsive differential equations with non-local condition via Time-changed Brownian motion followed by the currency options pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004813
    DOI: 10.1016/j.chaos.2025.116468
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    References listed on IDEAS

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    1. Zhou, Jun & Shen, Jun & Zhang, Weinian, 2020. "Growth in an impulsive integral inequality," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Xiuwei Yin & Wentao Xu & Guangjun Shen, 2021. "Stability of stochastic differential equations driven by the time-changed Lévy process with impulsive effects," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(11), pages 2338-2357, August.
    3. Kasinathan, Ramkumar & Kasinathan, Ravikumar & Chalishajar, Dimplekumar & Baleanu, Dumitru & Sandrasekaran, Varshini, 2024. "The averaging principle of Hilfer fractional stochastic pantograph equations with non-Lipschitz conditions," Statistics & Probability Letters, Elsevier, vol. 215(C).
    4. T. Sathiyaraj & JinRong Wang, 2024. "Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 995-1025, June.
    5. Li, Dingshi & Lin, Yusen, 2021. "Periodic measures of impulsive stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    6. Foad Shokrollahi & Adem Kılıçman & Marcin Magdziarz, 2016. "Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-22, March.
    7. Chalishajar, Dimplekumar & Kasinathan, Dhanalakshmi & Kasinathan, Ramkumar & Kasinathan, Ravikumar, 2024. "Exponential stability, T-controllability and optimal controllability of higher-order fractional neutral stochastic differential equation via integral contractor," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
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