Fractional Neutral Systems Research Articles

Results concerning to approximate controllability of non‐densely defined Sobolev‐type Hilfer fractional neutral delay differential system

In this manuscript, our primary focus on the approximate controllability outcomes for non‐densely defined Sobolev‐type Hilfer fractional neutral differential system with infinite delay. By applying the findings and facts associated with fractional theory and the fixed‐point method, the principal discussions are demonstrated. First, we focus on the existence and then discuss the approximate controllability. At last, we provide an example for the demonstration of theory.

Delay-independent stability criteria for RiemannLiouville s nonlinear fractional neutral systems: Adescriptor system approach

Delay-independent stability criteria for RiemannLiouville s nonlinear fractional neutral systems: Adescriptor system approach

A neutral fractional Halanay inequality and application to a Cohen–Grossberg neural network system

We extend the well‐known Halanay inequality to the fractional‐order case in presence of distributed delays and delays of neutral type (in the fractional derivative). Both the discrete and distributed neutral delays are investigated. It is proved that solutions decay toward zero in a Mittag–Leffler manner under some rather general conditions. Some large classes of kernels and examples satisfying our assumptions are provided. We apply our findings to prove Mittag–Leffler stability for solutions of fractional neutral network systems of Cohen–Grossberg type.

Stability of fractional neutral systems with time varying delay based on delay decomposition approach

Stability of fractional neutral systems with time varying delay based on delay decomposition approach

Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness

Abstract This manuscript highlights the controllability of Hilfer fractional neutral differential systems with infinite delay. A vivid study on the primary outcomes is carried out by applying fractional calculus, and for the main results, we use fixed point technique to the measures of noncompactness. The results, thus acquired, are extend to the concept of nonlocal conditions. Lastly, a model is presented for the illustration of theory.

Asymptotic stability of fractional neutral stochastic systems with variable delays

This paper mainly concerns with the stability of nonlinear Caputo fractional neutral stochastic differential system with variable delay. A sufficient condition is derived to ensure that the trivial solution is mean-square asymptotically stable by employing the Banach’s contraction principle, in which the boundedness of delays is not required. An illustrative example is provided to show the efficiency of our results.

Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

The aim of this work is to obtain an integral representation formula for the solutions of initial value problems for autonomous linear fractional neutral systems with Caputo type derivatives and distributed delays. The results obtained improve and extend the corresponding results in the particular case of fractional systems with constant delays and will be a useful tool for studying different kinds of stability properties. The proposed results coincide with the corresponding ones for first order neutral linear differential systems with integer order derivatives.

Stability and Synchronization of a Fractional Neutral Higher-Order Neural Network System

Abstract We discuss the stability and synchronization of some neural network systems with more than one feature. They are of higher-order, of fractional order and also involving delays of neutral type. Each one of these features presents substantial difficulties to overcome. We prove stability and synchronization of Mittag-Leffler type. This rate is fairly reasonable in case of fractional order. This leads us to prove a neutral fractional version of the well-known Halanay inequality which is interesting by itself. Another feature of the present work is the treatment of unbounded activation functions. The condition of uniform boundedness of the activation functions was commonly used in the literature.

Asymptotic Analysis of Linear and Interval Linear Fractional-Order Neutral Delay Differential Systems Described by the Caputo-Fabrizio Derivative

Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.

New results on Caputo fractional-order neutral differential inclusions without compactness

This article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theorems to obtain the existence of the solution. Furthermore, the results are manifested for fractional neutral system held by nonlocal conditions. To justify the application of the reported results an illustration is presented.

Further results on the asymptotic stability of Riemann\u2013Liouville fractional neutral systems with variable delays

In this paper, the investigation of the asymptotic stability of Riemann–Liouville fractional neutral systems with variable delays has been presented. The advantage of the Lyapunov functional was used to achieve the desired results. The stability criteria obtained for zero solution of the system were formulated as linear matrix inequalities (LMIs) which can be easily solved. The advantage of the considered method is that the integer-order derivatives of the Lyapunov functionals can be directly calculated. Finally, three numerical examples have been evaluated to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established assumptions by MATLAB-Simulink.

Asymptotical stability analysis of Riemann‐Liouville q‐fractional neutral systems with mixed delays

This paper investigates the asymptotical stability of Riemann‐Liouville q‐fractional neutral systems with mixed delays (constant time delay and distributed delay). By constructing some appropriate Lyapunov‐Kravsovskii functionals, some sufficient conditions on delay‐dependent and delay‐independent asymptotical stability are obtained in terms of linear matrix inequality (LMI). Our employed method is based on the direct calculation of quantum derivatives of the Lyapunov‐Kravsovskii functionals. Finally, two examples are presented to demonstrate the availability of our obtained 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.

Optimal feedback control for fractional neutral dynamical systems

In this paper, we consider feedback control systems governed by fractional neutral equations involving Riemann–Liouville derivatives. Firstly, we show the existence and uniqueness of solutions for the feedback control systems by applying Krasnoselskiis fixed point theorem. Then, we use Filippove theorem to obtain the existence of feasible pairs. Finally, an existence result of optimal control pairs for the Lagrange problem is proved.

A Unified Approach for the $H_\infty$-Stability Analysis of Classical and Fractional Neutral Systems with Commensurate Delays

A Unified Approach for the $H_\infty$-Stability Analysis of Classical and Fractional Neutral Systems with Commensurate Delays

Controllability and minimum energy control of fractional neutral delay system

In this paper, we consider a class of time invariant control system governed by the neutral delay differential equation of fractional order 1 < α ≤ 2. Necessary and sufficient conditions for the controllability of linear fractional neutral system is derived. The existence of solution and controllability for the proposed nonlinear system is obtained by using the successive approximation technique. Also, the minimum energy control problem of corresponding linear positive system is stated and proved by using the Grammian matrix approach. Finally two numerical examples are substantiated to illustrate the proposed theory.

Controllability of nonlinear stochastic neutral fractional dynamical systems

In this paper, we obtain an equivalent nonlinear integral equation to the stochastic neutral fractional system with bounded operator. Using the integral equation, the sufficient conditions for ensuring the complete controllability of the stochastic fractional neutral systems with Wiener and Lévy noise are obtained. Banach's fixed point theorem is used to obtain the results. Examples are provided to illustrate the theory.

Controllability of nonlinear stochastic fractional neutral systems with multiple time varying delays in control

Sufficient conditions for relative controllability of stochastic fractional neutral systems with bounded operator and multiple time varying delay in the control are obtained. The result is proved using an equivalent nonlinear integral equation to the system and Banach contraction principle. The controllability results are derived for systems with both Wiener and systems with Le´vy noise.

Asymptotical stability of Riemann–Liouville fractional neutral systems

In this paper, the asymptotical stability of Riemann–Liouville fractional neutral systems is investigated. Applying Lyapunov direct method, we present new sufficient conditions on asymptotical stability in terms of linear matrix inequality (LMI) which can be easily solved. The advantage of our employed method is that one may directly calculate integer-order derivatives of the Lyapunov functions. Finally, two simple examples are given to show that the proposed method is computationally flexible and efficient.

Stability Analysis of Linear Fractional-Order Neutral Systems with Time Delay

In this paper, we mainly study the Lyapunov asymptotical stability of linear and interval linear fractional order neutral systems with time delay. By applying the characteristic equations of these two systems, some simple sufficient Lyapunov asymptotical stability conditions are deserved, which are quite different from other ones in literature. In addition, some numerical examples are provided to demonstrate the effectiveness of our results.