A. Vinodkumar

EXISTENCE, UNIQUENESS AND STABILITY OF RANDOM IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract In this article, we study the existence, uniqueness, stability through continuous dependence on initial conditions and Hyers-Ulam-Rassias stability results for random impulsive fractional differential systems by relaxing the linear growth conditions. Finally, we give examples to illustrate its applications.

STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

Abstract In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.

Exponential stability results for fixed and random type impulsive Hopfield neural networks

This article presents the exponential stability results on impulsive Hopfield neural networks IHNNs via variation of parameters and fixed point theory. The study is mainly considering two types of IHNNs, namely fixed and random type IHNNs. A numerical example is also presented to validate the theoretical results.

Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions

We discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one. We, then, rely on fixed point theorems for multivalued operators to prove our main results.

Some results in stochastic functional integro-differential equations with infinite delays

In this paper, we study the results on averaging principle and stability of mild solutions for stochastic functional integro-differential equation with non-Lipschitz condition. We establish the result by the method of successive approximation and Biharis inequality under the theory of resolvent operators. Finally, an example is provided for demonstration.

Existence and stability solutions of nonlinear stochastic functional partial integrodifferential equations with infinite delay

In this paper, we are focused upon the results on existence, uniqueness and stability of mild solution for stochastic functional integrodifferential equations with non-Lipschitz condition. The theory of resolvent operator is utilised to exhibit the existence of these mild solutions. The results are obtained by using the method of successive approximation and Biharis inequality. Finally, an example is provided for demonstration.

Existence results for random impulsive neutral differential inclusions with lower semicontinuous

This article presents the results on existence of mild solutions for random impulsive neutral functional differential inclusions under sufficient conditions. The results are obtained by using the Krasnoselskii-Schaefer type fixed point theorem combined with the selection theorem of Berssan and Colombo for lower semicontinuous (LSC) maps with decomposable values.