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Volume 9
Issue 17
10.3390/math9172111
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Article

On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions

by
Ahmed M. A. El-Sayed
* and
Hoda A. Fouad
*
Faculty of Science, Alexandria University, Alexandria 21568, Egypt
*
Authors to whom correspondence should be addressed.
Mathematics 2021, 9(17), 2111; https://doi.org/10.3390/math9172111
Submission received: 3 July 2021 / Revised: 25 August 2021 / Accepted: 27 August 2021 / Published: 1 September 2021
(This article belongs to the Special Issue Advances in Delay Differential Equations)
Versions Notes

Abstract

It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering. Here we are concerned with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.
Keywords: stochastic processes; stochastic differential equation; coupled system; nonlocal stochastic integral conditions stochastic processes; stochastic differential equation; coupled system; nonlocal stochastic integral conditions

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MDPI and ACS Style

El-Sayed, A.M.A.; Fouad, H.A. On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions. Mathematics 2021, 9, 2111. https://doi.org/10.3390/math9172111

AMA Style

El-Sayed AMA, Fouad HA. On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions. Mathematics. 2021; 9(17):2111. https://doi.org/10.3390/math9172111

Chicago/Turabian Style

El-Sayed, Ahmed M. A., and Hoda A. Fouad. 2021. "On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions" Mathematics 9, no. 17: 2111. https://doi.org/10.3390/math9172111

APA Style

El-Sayed, A. M. A., & Fouad, H. A. (2021). On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions. Mathematics, 9(17), 2111. https://doi.org/10.3390/math9172111

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