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

Dimplekumar Chalishajar; Ramkumar Kasinathan; Ravikumar Kasinathan

doi:10.2478/tmmp-2024-0002

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

Tatra Mountains Mathematical Publications

Volume 88 (2024): Issue 3 (December 2024)

By: Dimplekumar Chalishajar, Ramkumar Kasinathan and Ravikumar Kasinathan

Open Access

|Mar 2024

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.

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