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Journal of Applied Nonlinear Dynamics 10(4) (2021) 695--707 | DOI:10.5890/JAND.2021.12.009

Sayooj Aby Jose$^{1,2}$ , Ashitha Tom$^3$, S. Abinaya$^4$, Weera Yukunthorn$^5$

$^{1}$ Ramanujan Centre for Higher Mathematics, Alagappa University, Tamil Nadu, India

$^{2}$ Department of Mathematics, Alagappa University, Tamil Nadu, India

$^{3}$ Department of Mathematics, Madurai Kamaraj University, Tamil Nadu, India

$^{4}$ Department of Mathematics, Rathinam College of Arts $&$ Science, Tamil Nadu, India

$^{5}$ Faculty of Science and Technology, Kanchanaburi Rajabhat University, Thailand

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Abstract

In this paper, we present existence and uniqueness of special random impulsive differential evolution equations with nonlocal condition in Hilbert spaces. Moreover we study the stability results for the same evolution equations. Existence and uniqueness results are proved using Banach fixed point theorem where as stability results using fixed point approach and semi group theory. Finally we give some applications of the nonlocal impulsive differential equations as well as evolution equations, which shows the importance of our theoretical results.

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