This paper is concerned with the controllability result of mild solution for an impulsive neutral fractional order stochastic integro-differential equation with infinite delay subject to nonlocal conditions. The existence result is obtained by using the fixed point technique on a Hilbert space. At last, we present an example to verify the result. MSC: 93B05 • 26A33 • 34K05 • 34A37 • 34K50

In this paper, by using fixed-point theorems, the existence and uniqueness of positive solutions to a class four-point impulsive fractional differential equations with p-Laplacian operators are studied. addition, three examples given justify conclusion. The interest paper is study operators.

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation techni...

This paper discusses the existence of solutions to antiperiodic boundary value problem for nonlinear impulsive fractional differential equations. By using Banach fixed point theorem, Schaefer fixed point theorem, and nonlinear alternative of Leray-Schauder type theorem, some existence results of solutions are obtained. An example is given to illustrate the main result.

In this investigation, our aim is to develop the definition of mild solutions for impulsive fractional differential equations of order α ∈ (1,2) and obtain some sufficient conditions for existence of mild solutions using the analytic operator functions and fixed point theorems. We also verify the existence result with an example involving partial derivative.

We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1.

In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

In this paper, a new class of abstract impulsive Riemann-Liouville fractional partial neutral functional differential equations with infinite delay is introduced. We apply the suitable fixed point theorem together with the Hausdorff measure of noncompactness to investigate the existence of mild solutions for these equations in Banach spaces. Finally, two examples to illustrate the applications ...

A class of fuzzy neural networks (FNNs) with time-varying delays and impulses is investigated.With removing some restrictions on the amplification functions, a new differential inequality is established, which improves previouse criteria. Applying this differential inequality, a series of new and useful criteria are obtained to ensure the existence of global robust attracting and invariant sets...