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Existence, Uniqueness and Stability of Neutral Stochastic Functional Integro-differential Evolution Equations with Infinite Delay

by C. Parthasarathy, A. Vinodkumar, M. Mallika Arjunan
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 65 - Number 15
Year of Publication: 2013
Authors: C. Parthasarathy, A. Vinodkumar, M. Mallika Arjunan
10.5120/10997-6174

C. Parthasarathy, A. Vinodkumar, M. Mallika Arjunan . Existence, Uniqueness and Stability of Neutral Stochastic Functional Integro-differential Evolution Equations with Infinite Delay. International Journal of Computer Applications. 65, 15 ( March 2013), 1-7. DOI=10.5120/10997-6174

@article{ 10.5120/10997-6174,
author = { C. Parthasarathy, A. Vinodkumar, M. Mallika Arjunan },
title = { Existence, Uniqueness and Stability of Neutral Stochastic Functional Integro-differential Evolution Equations with Infinite Delay },
journal = { International Journal of Computer Applications },
issue_date = { March 2013 },
volume = { 65 },
number = { 15 },
month = { March },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-7 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume65/number15/10997-6174/ },
doi = { 10.5120/10997-6174 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:18:52.553663+05:30
%A C. Parthasarathy
%A A. Vinodkumar
%A M. Mallika Arjunan
%T Existence, Uniqueness and Stability of Neutral Stochastic Functional Integro-differential Evolution Equations with Infinite Delay
%J International Journal of Computer Applications
%@ 0975-8887
%V 65
%N 15
%P 1-7
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This article presents the results on existence, uniqueness and stability of mild solutions to neutral stochastic functional evolution integro-differential equations with non-Lipschitz condition and Lipschitz condition. The existence of mild solutions for the equations are discussed by means of semigroup theory and theory of resolvent operator. Under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari's inequality. Moreover, an example is given to illustrate our results.

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Index Terms

Computer Science
Information Sciences

Keywords

Resolvent operator Evolution operator Existence Uniqueness Stability Successive approximation Bihari's inequality

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