<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential equations with the Rosenblatt process and Poisson jumps. The existence of mild solutions for the equations is discussed by means of the semigroup theory and theory of the resolvent operator. Next, under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Finally, an example is provided to illustrate our results.</p>
</abstract>

In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential equations with the Rosenblatt process and Poisson jumps. The existence of mild solutions for the equations is discussed by means of the semigroup theory and theory of the resolvent operator. Next, under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Finally, an example is provided to illustrate our results.

Existence and Stability Results for Time-Dependent Impulsive Neutral Stochastic Partial Integrodifferential Equations with Rosenblatt Process and Poisson Jumps

Department of Applied Mathematics, Mallory Hall

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential...

Existence and Stability Results for Time-Dependent Impulsive Neutral Stochastic Partial Integrodifferential Equations with Rosenblatt Process and Poisson Jumps

Published Online: Mar 12, 2024

Page range: -

Received: Sep 22, 2022

Accepted: Dec 03, 2023

DOI: https://doi.org/10.2478/tmmp-2024-0002

Keywords
resolvent operator, stochastic partial differential equations, Poisson jumps, fractional Brownian motion, successive approximation, Bihari’s inequality

© 2024 Dimplekumar Chalishajar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Existence and Stability Results for Time-Dependent Impulsive Neutral Stochastic Partial Integrodifferential Equations with Rosenblatt Process and Poisson Jumps

Published Online: Mar 12, 2024

Page range: -

Received: Sep 22, 2022

Accepted: Dec 03, 2023

DOI: https://doi.org/10.2478/tmmp-2024-0002

Keywordsresolvent operator, stochastic partial differential equations, Poisson jumps, fractional Brownian motion, successive approximation, Bihari’s inequality

© 2024 Dimplekumar Chalishajar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
resolvent operator, stochastic partial differential equations, Poisson jumps, fractional Brownian motion, successive approximation, Bihari’s inequality