Qualitative behaviour of stochastic integro-differential equations with random impulses

In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups in Hilbert spaces via resolvent operators. Initially, we prove the existence of mild solution for the system is established by using Mönch fixed point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results includes continuous dependence of solutions on initial conditions, exponential stability and Hyers–Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained resultsThe work of JJN has been partially supported by the Agencia Estatal de Investigacion (AEI) of Spain under Grant PID2020-113275GB-100, Co-financed by the Europen Community fund FEDER, as well as Xunta de Galicia grant ED431C 2019/02 for Competitive Reference Research Groups (2019-22). Open Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureS

Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse

Abstract The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated in this article. Initially, a random impulsive stochastic integrodifferential system is proposed and the existence of a mild solution for the system is established using the Mönch fixed-point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results including a continuous dependence of solutions on initial conditions, exponential stability, and Hyers–Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results

Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process

The purpose of this paper is to determine a class of neutral stochastic functional integro-differential system in real separable Hilbert spaces as well as the exponential stability results. The Rosenblatt process acts as the driving force behind the systems. Initially, the existence results for mild solutions of the stochastic system is investigated by using stochastic analysis, integro-differential theory, and fixed point theory. The analysis of the exponential stability of mild solutions to nonlinear neutral stochastic integro-differential systems driven by Rosenblatt process is the main objective of the investigation’s further stages. The system’s trajectory controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. Our work extends the work of Chalishajar et al. (2010), Chalishajar and Chalishajar (2015), Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022) where the pth moment exponential stability has not discussed. Also, numerical simulation has not studied in Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022)

Book of Abstracts of the 2nd International Conference on Applied Mathematics and Computational Sciences (ICAMCS-2022)

It is a great privilege for us to present the abstract book of ICAMCS-2022 to the authors and the delegates of the event. We hope that you will find it useful, valuable, aspiring, and inspiring. This book is a record of abstracts of the keynote talks, invited talks, and papers presented by the participants, which indicates the progress and state of development in research at the time of writing the research article. It is an invaluable asset to all researchers. The book provides a permanent record of this asset. Conference Title: 2nd International Conference on Applied Mathematics and Computational SciencesConference Acronym: ICAMCS-2022Conference Date: 12-14 October 2022Conference Organizers: DIT University, Dehradun, IndiaConference Mode: Online (Virtual