8 research outputs found
Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays
This article presents the results on existence, uniqueness and stability of mild solutions of impulsive stochastic semilinear neutral functional differential equations without a Lipschitz condition and with a Lipschitz condition. The results are obtained by using the method of successive approximations
Mild solutions of RiemannāLiouville fractional differential equations with fractional impulses
We consider RiemannāLiouville fractional differential equations with fractional-order derivative in the impulsive conditions. We study the existence of the mild solution by applying the Laplace transform method and (a,k)-regularized resolvent operator. We use the contraction mapping principle and fixed point theorem for condensing map to prove our existence results
Approximate Controllability of Semilinear Stochastic Integrodifferential System with Nonlocal Conditions
The objective of this paper is to analyze the approximate controllability of a semilinear stochastic integrodifferential system with nonlocal conditions in Hilbert spaces. The nonlocal initial condition is a generalization of the classical initial condition and is motivated by physical phenomena. The results are obtained by using Sadovskiiās fixed point theorem. At the end, an example is given to show the effectiveness of the result
A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces
In this paper, we study the problem of controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskiiās fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory
On neutral impulsive stochastic differential equations with Poisson jumps
Abstract We study the results of existence and continuous dependence on neutral impulsive stochastic differential equations with Poisson jumps. We have also created some conditions confirming exponential stability