Fractional Neutral Integro-differential Equations Research Articles

Existence Results of Fractional Neutral Integrodifferential Equations with Deviating Arguments

In this paper we prove the existence of solutions of fractional neutral integrodifferential equations with deviating arguments by using the resolvent operators and fixed point theorem. Examples are discussed to illustrate the theory.

Existence Results for Nonlinear Implicit Neutral Fractional Integrodifferential Equations with Nonlocal Condition

Existence Results for Nonlinear Implicit Neutral Fractional Integrodifferential Equations with Nonlocal Condition

A new exploration on existence of fractional neutral integro- differential equations in the concept of Atangana–Baleanu derivative

In this paper, we investigate a new fractional derivative with Mittag Leffler kernels (AB-derivative) to the fractional neutral integro-differential equations in Banach spaces. The results are based on fixed point theorems, then we implement a suitable examples and illustrate it by graphical methods with variation of fractional order.

Existence of mild solution for a class of coupled systems of neutral fractional integro-differential equations with infinite delay in Banach space

We deal with a class of coupled systems of neutral fractional integro-differential equations with infinite delay in a Banach space in this paper. Based on the Banach contraction principle and Krasnoselskii’s fixed point theorem, some new sufficient criteria are established to guarantee the existence of mild solutions. As an application, an example is given to illustrate the effectiveness of our main results.

Local existence for an impulsive fractional neutral integro-differential system with Riemann\u2013Liouville fractional derivatives in a Banach space

In this manuscript, we investigate a sort of fractional neutral integro-differential equations with impulsive outcomes and extend the formula of general solutions for the impulsive fractional neutral integro-differential system in a Banach space. By using the analysis of the limit case and the operator generating compact semigroup, we derive the main results. Finally, an example is discussed to illustrate the efficiency of the results.

Existence results of solutions for impulsive fractional differential equations

Abstract We analyze the existence of solution for the neutral fractional integro-differential equation (FDE) of order in the interval (1, 2] with impulsive and integral boundary conditions (IBCs). The key approach for outcomes are based on the non-compactness measures and fixed point techniques.We obtain some sufficient conditions on the existence of solutions for the proposed system. Moreover, some applications are studies to demonstrate the proficiency and utility of the main results.

Existence results for Hadamard and Riemann-Liouville functional fractional neutral integrodifferential equations with finite delay

By using Leray-Schauder?s alternative, we study the existence and uniqueness of solutions for some Hadamard and Riemann-Liouville fractional neutral functional integrodifferential equations with finite delay, whereas the uniqueness of the solution is established by Banach?s contraction principle. An illustrative example is also included.

Existence Results For Impulsive Fractional Neutral Integro-Differential Equations With Nonlocal Conditions

Existence Results For Impulsive Fractional Neutral Integro-Differential Equations With Nonlocal Conditions

Existence result for neutral fractional integrodifferential equations with nonlocal integral boundary conditions

Existence result for neutral fractional integrodifferential equations with nonlocal integral boundary conditions

Existence and exponential stability for neutral stochastic fractional differential equations with impulses driven by Poisson jumps

The paper is mainly concerned with a class of neutral stochastic fractional integro-differential equation with Poisson jumps. First, the existence and uniqueness for mild solution of an impulsive stochastic system driven by Poisson jumps is established by using the Banach fixed point theorem and resolvent operator. The exponential stability in the pth moment for mild solution to neutral stochastic fractional integro-differential equations with Poisson jump is obtained by establishing an integral inequality.

On the controllability of fractional neutral integrodifferential delay equations with nonlocal conditions

In this paper, by using the fractional calculus, measure of noncompactness, and the Mönch's fixed point theorem, we investigate the controllability results for fractional neutral integrodifferential equations with nonlocal conditions in Banach spaces. In the end, we give an example to illustrate the applications of the abstract conclusions. Copyright © 2017 John Wiley & Sons, Ltd.

A study on existence of solutions for fractional functional differential equations

In this research article, we establish the existence results of mild solutions for semi-linear impulsive neutral fractional order integro-differential equations with state dependent delay subject to nonlocal initial condition by applying well known classical fixed point theorems. At last, we present an example of partial derivative to illuminate the results.

Controllability Problem of Fractional Neutral Systems: A Survey

The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems.

Exact controllability and continuous dependence of fractional neutral integro-differential equations with state-dependent delay

In the present paper, with the help of the resolvent operator and some analytic methods, the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay. As an application, we also give one example to demonstrate our results.

Erratum to: Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay

Erratum to: Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay

Approximation of Solutions to Stochastic Neutral Fractional Integro-Differential Equation with Nonlocal Conditions

In this paper, we study a stochastic neutral fractional integro-differential equation with nonlocal conditions in separable Hilbert spaces. We obtain an associated integral equation and then, consider a sequence of approximate integral equations. We used the semigroup theory of linear operators and stochastic version of Banach fixed point theorem to study the existence and uniqueness of the mild solution for every approximate integral equation. Next, we show the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. Moreover, the Faedo–Galerkin approximation of solution is established. In the last, an example is provided to illustrate the applications of the abstract results.

Approximations of Solutions of a Neutral Fractional Integro-Differential Equation

In the present work, we consider a fractional integro-differential equation in an arbitrary separable Hilbert space H. An associated integral equation and a sequence of approximate integral equations is studied. The existence and uniqueness of solutions to every approximate integral equation is obtained by using analytic semigroup and Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We show the convergence of the solutions using Faedo–Galerkin approximation and demonstrate some convergence results. Finally, an example is considered to show the effectiveness of the obtained theory.

Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay

In this paper, we obtain a set of sufficient conditions to prove the approximate controllability for a class of nonlocal neutral fractional integro-differential equations, with time varying delays, considered in a Hilbert space. We also establish the existence of a mild solution of the system. The main tools used in our analysis are the theory of analytic semigroups, the theory of fractional powers of operators, ?-norm, fractional calculus, and Krasnoselskii's fixed point theorem. An example is provided to illustrate the applicability of the main results.

Existence results for an impulsive neutral stochastic fractional integro-differential equation with infinite delay

In this work, we consider an impulsive neutral stochastic fractional integro-differential equation with infinite delays in an arbitrary separable Hilbert space. The existence of mild solution is obtained by using resolvent operator and fixed point theorems. An example is considered to illustrate the theory and conclusion is also provided at the end of the manuscript.

Asymptotically Almost Automorphic Solutions of Fractional Order Neutral Integro-Differential Equations

In this paper, we study the existence of asymptotic almost automorphic solution of fractional neutral integro-differential equation. We prove the result using fixed-point theorems. We show the result with Lipschitz condition and without Lipschitz condition on the forcing term. Finally, examples are given to illustrate the analytical findings.