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

2021 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Foued
Keyword(s):  
Differential Equations ◽  
Continuous Dependence ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Nonlinear Differential Equations ◽  
Nonlocal Conditions ◽  
Coupled System ◽  
Coupled Systems ◽  
Integral Conditions ◽  
Uniqueness Of The Solution

Here we are concerning 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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2111
Author(s):  
Ahmed M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlocal Conditions ◽  
Integral Condition ◽  
Coupled System ◽  
Coupled Systems ◽  
Integral Conditions ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Condition

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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2571
Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Integral ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Nonlocal Problems ◽  
Integral Conditions ◽  
Fractional Stochastic Differential Equations ◽  
Random Integral

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 Ito^-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.

scholarly journals The existence and properties of the solution of a class of nonlinear differential equations with switching at variable times

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Huanting Li ◽  
Yunfei Peng ◽  
Kuilin Wu
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Initial State ◽  
Switching Line ◽  
Uniqueness Of The Solution ◽  
The Stability ◽  
Necessary And Sufficient

<p style='text-indent:20px;'>In this paper, we deal with the qualitative theory for a class of nonlinear differential equations with switching at variable times (SSVT), such as the existence and uniqueness of the solution, the continuous dependence and differentiability of the solution with respect to parameters and the stability. Firstly, we obtain the existence and uniqueness of a global solution by defining a reasonable solution (see Definition 2.1). Secondly, the continuous dependence and differentiability of the solution with respect to the initial state and the switching line are investigated. Finally, the global exponential stability of the system is discussed. Moreover, we give the necessary and sufficient conditions of SSVT just switching <inline-formula><tex-math id="M1">\begin{document}$ k\in \mathbb{N} $\end{document}</tex-math></inline-formula> times on bounded time intervals.</p>

scholarly journals Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Mohamed Hannabou ◽  
Hilal Khalid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Coupled Systems ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

The study of coupled systems of hybrid fractional differential equations requires the attention of scientists for the exploration of their different important aspects. Our aim in this paper is to study the existence and uniqueness of the solution for impulsive hybrid fractional differential equations. The novelty of this work is the study of a coupled system of impulsive hybrid fractional differential equations with initial and boundary hybrid conditions. We used the classical fixed-point theorems such as the Banach fixed-point theorem and Leray–Schauder alternative fixed-point theorem for existence results. We also give an example of the main results.

scholarly journals Investigating a Coupled Hybrid System of Nonlinear Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wiyada Kumam ◽  
Mian Bahadur Zada ◽  
Kamal Shah ◽  
Rahmat Ali Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Point Boundary ◽  
Coupled Fixed Point Theorem ◽  
Fractional Differential

We study sufficient conditions for existence of solutions to the coupled systems of higher order hybrid fractional differential equations with three-point boundary conditions. For this motive, we apply the coupled fixed point theorem of Krasnoselskii type to form adequate conditions for existence of solutions to the proposed system. We finish the paper with suitable illustrative example.

Sign in / Sign up

Export Citation Format

Share Document