Browsing by Author "Kasinathan, Ramkumar"

Now showing 1 - 7 of 7

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: 4
Citation - Scopus: 4
Existence and Hyers-Ulam Stability of Stochastic Integrodifferential Equations With a Random Impulse
(Springer, 2023) Kasinathan, Ravikumar; Sandrasekaran, Varshini; Baleanu, Dumitru; Kasinathan, Ramkumar
The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated in this article. Initially, a random impulsive stochastic integrodifferential system is proposed and the existence of a mild solution for the system is established using the Monch fixed-point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results including a continuous dependence of solutions on initial conditions, exponential stability, and Hyers-Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results.
Citation - WoS: 7
Citation - Scopus: 9
Existence, Uniqueness and Hyers-Ulam Stability of Random Impulsive Stochastic Integro-Differential Equations With Nonlocal Conditions
(Amer inst Mathematical Sciences-aims, 2022) Kasinathan, Ramkumar; Kasinathan, Ravikumar; Sandrasekaran, Varshini; Baleanu, Dumitru
In this article, we study the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups and resolvent operators in Hilbert spaces. Initially, we prove the existence of mild solutions using Hausdorff measures of noncompactness and Mo spacing diaeresis nch fixed point theorem. Then, we explore the stability results which includes continuous dependence of initial conditions, Hyers-Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, we propose an example to validate the obtained results.
Citation - WoS: 14
Citation - Scopus: 13
Hilfer Fractional Neutral Stochastic Differential Equations With Non-Instantaneous Impulses
(Amer inst Mathematical Sciences-aims, 2021) Kasinathan, Ravikumar; Baleanu, Dumitru; Annamalai, Anguraj; Kasinathan, Ramkumar
The aim of this manuscript is to investigate the existence of mild solution of Hilfer fractional neutral stochastic differential equations (HFNSDEs) with non-instantaneous impluses. We establish a new criteria to guarantee the sufficient conditions for a class of HFNSDEs with non-instantaneous impluses of order 0 < beta < 1 and type 0 <= alpha <= 1 is derived with the help of semigroup theory and fixed point approach, namely Monch fixed point theorem. Finally, a numerical example is provided to validate the theoretical results.
Hyers-Ulam Stability of Fractional Stochastic Differential Equations With Random Impulse
(Korean Mathematical Soc, 2023) Baleanu, Dumitru; Kandasamy, Banupriya; Kasinathan, Ramkumar; Kasinathan, Ravikumar; Sandrasekaran, Varshini
The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.
Citation - WoS: 2
Citation - Scopus: 2
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.
Citation - WoS: 2
Citation - Scopus: 3
Well Posedness of Second-Order Impulsive Fractional Neutral Stochastic Differential Equations
(Amer inst Mathematical Sciences-aims, 2021) Kasinathan, Ravikumar; Baleanu, Dumitru; Annamalai, Anguraj; Kasinathan, Ramkumar
In this manuscript, we investigate a class of second-order impulsive fractional neutral stochastic differential equations (IFNSDEs) driven by Poisson jumps in Banach space. Firstly, sufficient conditions of the existence and the uniqueness of the mild solution for this type of equations are driven by means of the successive approximation and the Bihari's inequality. Next we get the stability in mean square of the mild solution via continuous dependence on initial value.