<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

Publié en ligne: 12 mars 2024

Pages: -

Reçu: 22 sept. 2022

Accepté: 03 déc. 2023

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

Mots clés
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

Publié en ligne: 12 mars 2024

Pages: -

Reçu: 22 sept. 2022

Accepté: 03 déc. 2023

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

Mots clésresolvent 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.

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