Browsing by Author "Chalishajar, Dimplekumar"

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Citation - WoS: 9
Citation - Scopus: 11
The Averaging Principle of Hilfer Fractional Stochastic Pantograph Equations With Non-Lipschitz Conditions
(Elsevier, 2024) Kasinathan, Ramkumar; Kasinathan, Ravikumar; Chalishajar, Dimplekumar; Baleanu, Dumitru; Sandrasekaran, Varshini
This paper is devoted to presenting an averaging principle for Hilfer fractional stochastic differential pantograph equations (HFSDPEs). The probability of the solutions to averaged stochastic systems in the means square sence can be used to approximate the solutions to HFSDPEs under appropriate non-Lipschitz conditions. Furthermore, certain previous results have been significantly generalised by our results. Finally, an example is given to demonstrate the feasibility of the results.
Citation - WoS: 3
Citation - Scopus: 4
Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by Fbm With Noncompact Semigroup Via Mönch Fixed Point
(Springer Basel Ag, 2024) Kasinathan, Ramkumar; Kasinathan, Ravikumar; Chalishajar, Dimplekumar; Sandrasekaran, Varshini; Baleanu, Dumitru
The aim of this work is to study the mild solutions for a class of impulsive neutral stochastic functional integrodifferential equations driven by fractional Brownian motion using noncompact semigroup in a Hilbert space. We assume that the linear part has a resolvent operator not necessarily compact but the operator norm is continuous. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Monch fixed point theorem. Furthermore, under some suitable assumptions, the considered system's trajectory (T-) controllability is established using generalized Gronwall's inequality. An example is delivered to illustrate the obtained theoretical results. Finally, real life fermentation example is discussed to supporting the proposed system.