Order Impulsive Differential Equations Research Articles

Asymptotic behavior of second order neutral differential equation with positive and negative coefficients and impulses effects

The paper focused on the asymptotic behavior property of solutions of the second order impulsive neutral differential equations with positive and negative coefficients and with impulsive integral term. Some sufficient conditions have been secured to ensure that all nonoscillatory solutions converge to zero. Illustrative examples were awarded for the main results.

Existence Results of Damped Second Order Impulsive Functional Differential Equations with Infinite Delay

Using the Monch fixed point theorem and progressive estimation method, we study the existence, uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces. The compactness assumption on associated family of operators and the impulsive term, some restrictive conditions on a priori estimation, noncompactness measure estimation and the impulsive term have not been used, our results are different from some known results. Finally, a noncompact semigroup example explains the obtained results.

Property of oscillation of first order impulsive neutral differential equations with positive and negative coefficients

In this paper, necessary and sufficient conditions for oscillation are obtained, so that every solution of the linear impulsive neutral differential equation with variable delays and variable coefficients oscillates. Most of authors who study the oscillatory criteria of impulsive neutral differential equations, investigate the case of constant delays and variable coefficients. However the points of impulsive in this paper are more general. An illustrate example is given to demonstrate our claim and explain the results.

Multiple periodic solutions for second order impulsive delay differential equations

In this paper we discuss the existence of periodic solutions for an impulsive nonautonomous second order delay differential equation. We obtain multiple periodic solutions by a variational approach.

Existence results for fractional order impulsive functional differential equations with multiple delays

In this paper, we study the solution of impulsive fractional differential equations with multiple delays by using the nonlinear alternative of Leray–Schauder and the Banach fixed point method. Also, we prove that the equations have at least one solution or unique solution with certain conditions. In the last part, we give two examples to illustrate the usefulness of the main results.

Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

Abstract This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.

General solutions of higher order impulsive fractional differential equations involved with the Caputo type generalized fractional derivatives and applications

General solutions of higher order impulsive fractional differential equations involved with the Caputo type generalized fractional derivatives and applications

Oscillation of Even Order Impulsive Neutral Partial Differential Equations with Distributed Deviating Arguments

In this paper, we will consider a class of boundary value problems associated with even order nonlinear impulsive neutral partial functional differential equations with continuous distributed deviating arguments. Sufficient conditions are obtained for the oscillation of solutions using impulsive differential inequalities and integral averaging scheme with pair of boundary conditions. Examples are specified to point up our important results.

A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations

A survey for studies on boundary value problems of higher order ordinary differential equations is given firstly. Secondly a simple review for studies on solvability of boundary value problems for impulsive fractional differential equations is presented. Thirdly by using a general method for converting an impulsive fractional differential equation with the Riemann-Liouville fractional derivatives to an equivalent integral equation and employing fixed point theorems in Banach space, we establish existence results of solutions for three classes of boundary value problems ($(n,n-k)$ type BVPs) of impulsive higher order fractional differential equations. Some examples are presented to illustrate the efficiency of the results obtained and some mistakes are also corrected at the end of the paper finally. A conclusion section is given at the end of the paper.

New boundary value problems for higher order impulsive fractional differential equations and their solvability

New boundary value problems for higher order impulsive fractional differential equations and their solvability

New boundary value problems for higher order impulsive fractional differential equations and their solvability

New boundary value problems for higher order impulsive fractional differential equations and their solvability

Solvability of boundary value problem for second order impulsive differential equations with one-dimensional p-Laplacian on whole line

This paper is concerned with a class of boundary value problems of the impulsive differential equations with one-dimensional p-Laplacian on whole line with a nonCarathéeodory nonlinearity. Sufficient conditions to guarantee the existence of solutions are established. Some examples are given to illustrate the main results.

On piecewise continuous solutions of higher order impulsive fractional differential equations and applications

For impulsive differential equations with fractional order, we show that the formula of solutions in cited papers are incorrect. We then give exact piecewise continuous solutions (the explicit solutions) of two classes of fractional differential equations of order α∈(n−1,n) involving Caputo derivatives and Riemann–Liouville derivatives. Apply our results to obtain existence of solutions of two classes of initial value problems of singular impulsive fractional differential equations. Examples are presented to illustrate the main theorems.

Existence of multiple solutions of some second order impulsive differential equations

This paper uses critical point theory and variational methods to investigate the multiple solutions of a boundary value problem for second order impulsive differential equations. The conditions for the existence of multiple solutions are established.

Impulsive retarded fractional differential equations with variable moments

Integer order impulsive functional differential equations with fi xed and variable times and the fractional order ones with fi xed times have been studied in the related literature several times, so far. To the extent we know, the fractional order ones with variable times have not yet been considered. In this work, we deal with establishing some existence results for solutions of impulsive retarded functional differential equations of fractional order with variable moments.

Solvability of boundary value problems for second order impulsive differential equations on whole line with a non-Carathédory nonlinearity

We study a class of boundary value problems of the impulsive differential equations on whole lines with a non-Carathéodory nonlinearity. Sufficient conditions to guarantee the existence of solutions are established. A new Banach function space X and its relatively compact property of subset of X is proved. An example is given to illustrate the main results.

Controllability study on fractional order impulsive stochastic differential equation∗∗The work was supported by National Board for Higher Mathematics, Mumbai, India under the grant No: 2/48(5)/2013/NBHM (R.P.)/RD-II/688 dt 16.01.2014.

Abstract In this paper, we consider a fractional order stochastic differential system with impulsive conditions. The necessary and sufficient conditions for the controllability of associated linear stochastic system is studied by using the controllability Grammian matrix defined by Mittag-Leffler function. The sufficient condition for controllability of the proposed nonlinear system is proved by using Banach fixed point theorem. An example is provided to illustrate the theory using the numerical integration by Haar wavelet approximation method.

Numerical Solution of Impulsive Fuzzy Initial Value Problem by Modified Euler's Method

In this paper we present numerical solution of first order impulsive fuzzy differential equation by modified Euler's method for the first time. The algorithm is discussed in detail and the result of the numerical solution is given by solving the numerical example and the graph is plotted finally.

Boundary value problem for the second order impulsive delay differential equations

Abstract We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order with impulses at fixed points.

Positive periodic solutions for second order differential equations with impulsive effects

The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using a fixed point theorem in cone, we obtain two existence results, which extend some known results.