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On a Coupled System of Stochastic It o ^ -Differential and the Arbitrary (Fractional) Order Differential Equations with Nonlocal Random and Stochastic Integral Conditions

Author

Listed:
  • A. M. A. El-Sayed

    (Faculty of Science, Alexandria University, Alexandria 21568, Egypt
    These authors contributed equally to this work.)

  • Hoda A. Fouad

    (Faculty of Science, Alexandria University, Alexandria 21568, Egypt
    These authors contributed equally to this work.)

Abstract

The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance. Here, we are concerned with the combination between the three senses of derivatives, the stochastic It o ^ -differential and the fractional and integer orders derivative for the second order stochastic process in two nonlocal problems of a coupled system of two random and stochastic differential equations with two nonlocal stochastic and random integral conditions and a coupled system of two stochastic and random integral conditions. We study the existence of mean square continuous solutions of these two nonlocal problems by using the Schauder fixed point theorem. We discuss the sufficient conditions and the continuous dependence for the unique solution.

Suggested Citation

  • A. M. A. El-Sayed & Hoda A. Fouad, 2021. "On a Coupled System of Stochastic It o ^ -Differential and the Arbitrary (Fractional) Order Differential Equations with Nonlocal Random and Stochastic Integral Conditions," Mathematics, MDPI, vol. 9(20), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2571-:d:655668
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    References listed on IDEAS

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    1. P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
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