Existence and controllability results for an impulsive stochastic integro-differential equations with state-dependent delay

Mamadou Abdoul Diop; Mbarack Fall; Firmin  Bodjrenou; Carlos Ogouyandjou

doi:10.26637/mjm1101/004

Abstract

In this article, we discuss the existence of mild solutions for a class of impulsive stochastic integro-differential equations with state-dependent delay in a real Hilbert space as well as the controllability of these solutions. These equations are posed in a real Hilbert space. In the beginning, we use the theory of resolvent operators in the sense of Grimmer and fixed point theory to show that there is a mild solution to the problem. The controllability of the mild solution is the next aspect of the problem that we will investigate in more depth. At the end of the article, a case study is used to show how the abstract findings of the research can be used.

Keywords:

Existence, Controllability, résolvent operator, impulsive stochastic integro-differential equations, semigroup theory, fixed point theorems, State-dependent delay

Mathematics Subject Classification:

34K50, 34K45, 93B05

Authors Imprint References Funding Related Articles Downloads

Mamadou Abdoul Diop Université Gaston Berger de Saint-Louis, UFR SAT, Département de Mathématiques, B.P. 234, Saint-Louis, Sénégal.
Mbarack Fall Université Gaston Berger de Saint-Louis, UFR SAT, Département de Mathématiques, B.P. 234, Saint-Louis, Sénégal.
Firmin Bodjrenou Institut de Mathématiques et de Sciences Physiques, URMPM B.P. 613, Porto-Novo, Bénin.
Carlos Ogouyandjou Institut de Mathématiques et de Sciences Physiques, URMPM B.P. 613, Porto-Novo, Bénin. https://orcid.org/0000-0001-7115-7724

Pages: 43-65
Date Published: 01-01-2023
Vol. 11 No. 01 (2023): Malaya Journal of Matematik (MJM)

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