Neutral Integro-differential Equations Research Articles

Existence and stability of mild solutions to non autonomous impulsive stochastic neutral integrodifferential equations

Existence and stability of mild solutions to non autonomous impulsive stochastic neutral integrodifferential equations

Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel

This manuscript examines the problem of nonlinear stochastic fractional neutral integro-differential equations with weakly singular kernels. Our focus is on obtaining precise estimates to cover all possible cases of Abel-type singular kernels. Initially, we establish the existence, uniqueness, and continuous dependence on the initial value of the true solution, assuming a local Lipschitz condition and linear growth condition. Additionally, we develop the Euler-Maruyama method for numerical solution of the equation and prove its strong convergence under the same conditions as the well-posedness. Moreover, we determine the accurate convergence rate of this method under global Lipschitz conditions and linear growth conditions.

Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions

We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by using fixed-point theorems, we establish the existence of mild solutions under more relaxed conditions.

A Study on Stochastic Neutral Integro-differential Equations with Infinite Delays: Mixed Fractional Brownian Motion and Poisson Jumps

A Study on Stochastic Neutral Integro-differential Equations with Infinite Delays: Mixed Fractional Brownian Motion and Poisson Jumps

On neutral integrodifferential equations with state-dependent delay in Banach spaces

On neutral integrodifferential equations with state-dependent delay in Banach spaces

Periodic Boundary Value problem for the Dynamical system with neutral integro-differential equation on time scales

Examining the results of existence and Ulam stability in a fractional dynamic system, including a neutral integro-differential equation that incorporates periodic boundary conditions on time scales and the Caputo fractional nabla derivative, is the main objective of the study. Standard fixed-point techniques are applied to obtain the results. Additionally, controllability and Ulam stability results are included. The application of the theoretical results is illustrated with a suitable example.

Investigation on continuous dependence and regularity solutions of functional integrodifferential equations

In this work, to show the existence and continuous dependence of integral solution for neutral integro-differential equation with finite delay situation. This result established by using integrated resolvent operator with support of Lipschitz continuous and uniqueness part using Banach contraction mapping. Also study the existence of strict solution on reflexive and general Banach spaces. In the last section, an example is provided related to this theory.

Impulsive Nonlocal Neutral Integro-Differential Equations Controllability results on Time Scales

Impulsive Nonlocal Neutral Integro-Differential Equations Controllability results on Time Scales

Explicit abstract neutral differential equations with state-dependent delay: Existence, uniqueness and local well-posedness

We study the local and global existence and uniqueness of strict solution and the local well-posedness for a class of abstract “explicit” neutral integro-differential equations with state-dependent delay. In the last section some examples motivated by explicit neutral ordinary integro-differential equations arising in the theory of population dynamics are presented.

Approximate Controllability of Neutral Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulses

In this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay. Our methodology relies on the utilization of resolvent operators in conjunction with Darbo’s fixed point theorem. To exemplify the practical implications of our findings, we provide an illustration.

Asymptotic stability of nonlinear neutral delay integro-differential equations

Abstract In this paper, by using Sadovskii’s fixed point theorem and the properties of the measure of noncompactness, we establish some sufficient conditions for the asymptotic stability results of nonlinear neutral integro-differential equations with variable delays. The results presented in this paper improve and generalize some results in the literature. An example is considered to illustrate our main results.

Interpretation on nonlocal neutral functional differential equations with delay

<abstract><p>This work deals with the existence and continuous dependence of an integral solution for neutral integro-differential equations with a nonlocal condition. This result is established by using an integrated resolvent operator under conditions of Lipschitz continuity and uniqueness via the Banach fixed point technique. We also study the existence of a strict solution on reflexive and general Banach spaces. In the last section, an example is provided related to this theory.</p></abstract>

On explicit abstract neutral differential equations with state-dependent delay

We introduce and study a class of abstract neutral differential equations with state-dependent delay at the temporal derivative. We study the local and global existence and uniqueness of mild solution and the existence of strict solution. Some examples concerning partial neutral integro-differential equations are presented.

CONTROLLABILITY OF SEMILINEAR NEUTRAL STOCHASTIC INTEGRODIFFERENTIAL EVOLUTION SYSTEMS WITH FRACTIONAL BROWNIAN MOTION

This paper focuses on the approximate controllability of semilinear neutral stochastic integrodifferential systems with fractional Brownian motion in a Hilbert space. The theory of analytic resolvent operators of linear neutral integrodifferential equations and the Banach fixed point theorem are employed to obtain the main results. In order to improve the regularity of solutions, the theory of fractional powers and the α-norm are also utilized to discuss the problem. An example is presented in the end to illustrate the applications of the obtained results.

Existence and Differentiability of Solutions for Nondensely Defined Neutral Integro-Differential Evolution Equations

Existence and Differentiability of Solutions for Nondensely Defined Neutral Integro-Differential Evolution Equations

Stability result for fractional fuzzy neutral integro-differential equations

Stability result for fractional fuzzy neutral integro-differential equations

Optimal control for Hilfer fractional neutral integrodifferential evolution equations with infinite delay

AbstractThe optimal control solutions for Hilfer fractional neutral integrodifferential evolution equations with infinite delay in Banach space are investigated in this study. To begin, we use fractional computations, Holder inequality, and Banach fixed point approaches to examine conclusions for fractional integrodifferential evolution equations. Following that, we created the fractional integrodifferential evolution system's continuous dependency. We also looked at optimal controls for the Lagrange problem. Finally, an application is given to extract the primary theory.

Neutral Stochastic Impulsive Integro-Differential Equations Driven by Fractional Brownian Motion and Brownian Motion with Nonlocal Condition

Neutral Stochastic Impulsive Integro-Differential Equations Driven by Fractional Brownian Motion and Brownian Motion with Nonlocal Condition

Stability Results of Some Fractional Neutral Integrodifferential Equations with Delay

Differential equations with fractional derivative are being extensively used in the modelling of the transmission of many infective diseases like HIV, Ebola, and COVID-19. Analytical solutions are unreachable for a wide range of such kind of equations. Stability theory in the sense of Ulam is essential as it provides approximate analytical solutions. In this article, we utilize some fixed point theorem (FPT) to investigate the stability of fractional neutral integrodifferential equations with delay in the sense of Ulam-Hyers-Rassias (UHR). This work is a generalized version of recent interesting works. Finally, two examples are given to prove the applicability of our results.

Existence and Asymptotic Periodicity of Solutions for Neutral Integro-Differential Evolution Equations with Infinite Delay

Abstract In this work, making use of the theory of resolvent operators and Banach fixed point theorem, we first discuss the existence and regularity of mild solutions for neutral partial functional integro-differential equations with infinite delay. We assume that the linear part of the considered equation generates a resolvent operator and the nonlinear function satisfies Lipschitz conditions. Then we investigate the asymptotic periodicity of mild solutions under asymptotic periodic assumption on the nonlinear function. The obtained results extend somewhat the related conclusions in literature. In the end, an example is presented to illustrate the obtained results.