Existence and Stability Results for Second-Order Neutral Stochastic Differential Equations With Random Impulses and Poisson Jumps

The objective of this paper is to investigate the existence and stability results of secondorder neutral stochastic functional differential equations (NSFDEs) in Hilbert space. Initially, we establish the existence results of mild solutions of the aforementioned system using the Banach contraction principle. The results are formulated using stochastic analysis techniques. In the later part, we investigate the stability results through the continuous dependence of solutions on initial conditions.

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Existence and Stability Results of Impulsive Stochastic Partial Neutral Functional Differential Equations with Inﬁnite Delays and Poisson Jumps

The interdisciplinary journal of Discontinuity Nonlinearity and Complexity ◽

10.5890/dnc.2020.06.006 ◽

2020 ◽

Vol 9 (2) ◽

pp. 245-255 ◽

Cited By ~ 2

Author(s):

A. Anguraj ◽

K. Ravikumar

Keyword(s):

Differential Equations ◽

Functional Differential Equations ◽

Poisson Jumps ◽

Neutral Functional Differential Equations ◽

Infinite Delays ◽

Existence And Stability ◽

Functional Differential ◽

Stability Results

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On Some Qualitative Properties of Mild Solutions of Nonlocal Semilinear Functional Differential Equations

Demonstratio Mathematica ◽

10.2478/dema-2014-0069 ◽

2014 ◽

Vol 47 (4) ◽

Author(s):

Rupali S. Jain ◽

M. B. Dhakne

Keyword(s):

Differential Equations ◽

Mild Solutions ◽

Semigroup Theory ◽

Functional Differential Equations ◽

Qualitative Properties ◽

Contraction Theorem ◽

Banach Contraction ◽

Functional Differential ◽

Banach Contraction Theorem ◽

Equations With Delay

AbstractIn the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.

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Global existence and stability results for mild solutions of random impulsive partial integro-differential equations

Filomat ◽

10.2298/fil1802439v ◽

2018 ◽

Vol 32 (2) ◽

pp. 439-455 ◽

Cited By ~ 1

Author(s):

A. Vinodkumar ◽

P. Indhumathi

Keyword(s):

Fixed Point ◽

Global Existence ◽

Differential Equations ◽

Continuous Dependence ◽

Fixed Point Theory ◽

Mild Solutions ◽

Point Theory ◽

Banach Contraction ◽

Existence And Stability ◽

Stability Results

In this paper, we discuss the global existence, uniqueness, continuous dependence and exponential stability of random impulsive partial integro-differential equations is investigated. The results are obtained by using the Leray-Schauder alternative fixed point theory and Banach Contraction Principle. Finally we give an example to illustrate our abstract results.

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On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽

10.2298/fil1702451b ◽

2017 ◽

Vol 31 (2) ◽

pp. 451-460 ◽

Cited By ~ 1

Author(s):

Mohammed Belmekki ◽

Kheira Mekhalfi

Keyword(s):

Differential Equations ◽

Measure Of Noncompactness ◽

Mild Solutions ◽

Functional Differential Equations ◽

Kuratowski Measure Of Noncompactness ◽

State Dependent ◽

State Dependent Delay ◽

Liouville Fractional Derivative ◽

Fractional Differential ◽

Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

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