共查询到20条相似文献,搜索用时 19 毫秒
1.
This paper deals with the existence of mild L-quasi-solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established. The results improve and extend some relevant results in ordinary differential equations and partial differential equations. An example is also given. 相似文献
2.
We study the multiplicity of solutions for a class of fractional differential equations influenced by both instantaneous and non-instantaneous impulses, subject to Neumann boundary conditions. A key contribution of this paper is that we have established a new variational structure and successfully applied critical point theory to investigate the impulsive fractional Neumann boundary value problem. By using the critical point theorem, we give some new criteria to guarantee that the impulsive problem has at least three solutions. An example is also given to illustrate the main results. 相似文献
3.
Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations
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In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed‐point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
Michal Fec?kan JinRong Wang 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):3050-3060
This paper is motivated from some recent papers treating the problem of the existence of a solution for impulsive differential equations with fractional derivative. We firstly show that the formula of solutions in cited papers are incorrect. Secondly, we reconsider a class of impulsive fractional differential equations and introduce a correct formula of solutions for a impulsive Cauchy problem with Caputo fractional derivative. Further, some sufficient conditions for existence of the solutions are established by applying fixed point methods. Some examples are given to illustrate the results. 相似文献
5.
JinRong Wang Michal Fec̆kan Yong Zhou 《Journal of Optimization Theory and Applications》2013,156(1):13-32
In this paper, we study optimal relaxed controls and relaxation of nonlinear fractional impulsive evolution equations. Firstly, existence of piecewise continuous mild solutions for the original fractional impulsive control system is presented. Secondly, fractional impulsive relaxed control system is constructed by using a regular countably additive measure and making the original control system convexified. Thirdly, optimal relaxed controls and relaxation theorems are obtained. Finally, application to initial-boundary value problem of fractional impulsive parabolic control system is considered. 相似文献
6.
《Mathematische Nachrichten》2018,291(2-3):443-491
In this paper, we propose the concepts of Caputo fractional derivatives and Caputo type Hadamard fractional derivatives for piecewise continuous functions. We obtain general solutions of four classes of impulsive fractional differential equations (Theorem 3.1–Theorem 3.4) respectively. These results are applied to converting boundary value problems for impulsive fractional differential equations to integral equations. Some comments are made on recently published papers (see Section 4). 相似文献
7.
《数学物理学报(B辑英文版)》2017,(5)
We study a generalized Cauchy problem associated with a class of impulsive fractional differential inclusions of Sobolev type in Banach spaces. Our aim is to prove the existence of a compact set of globally attracting solutions to the problem in question. An application to fractional partial differential equations subject to impulsive effects is given to illustrate our results. 相似文献
8.
This paper is inspired by the recent papers on the BVP for impulsive fractional differential equations. We present a general framework to find the solutions of anti-periodic BVP for linear impulsive fractional differential equations with constant coefficients. Some sufficient conditions for existence of the solutions for nonlinear problem are established. Finally, numerical examples are given to illustrate the results. 相似文献
9.
Haihua Wang 《Journal of Applied Mathematics and Computing》2012,38(1-2):85-101
In this paper, we discuss some existence results for a class of multi-point boundary value problem for impulsive fractional functional differential equations. Some sufficient conditions are obtained by using suitable fixed point theorems. Examples are also given to illustrate our results. 相似文献
10.
《Optimization》2012,61(6):827-840
In this article, the second-order nonlinear impulsive evolution differential equations with time-varying generating operators is considered. Constructing evolution systems generated by time-varying operator matrix, we introduce suitable mild solution of the second-order nonlinear impulsive evolution differential equations. The existence and uniqueness of the mild solutions and the continuous dependence on initial value are proved. The existence of the optimal controls for a Lagrange problem of the systems governed by the second-order nonlinear impulsive evolution equations is also presented. An example is given for demonstration. 相似文献
11.
Mixed Boundary Value Problems for a Class of Fractional Differential Equations with Impulses
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We investigate a class of mixed boundary value problem of nonlinear impulsive fractional differential
equations with a parameter. The uniqueness of this problem is proved by applying Banach fixed point theorem. 相似文献
12.
通过Schauder不动点定理和Banach压缩映射原理得到了一类非线性分数阶脉冲微分方程边值问题解的存在性和唯一性结果. 相似文献
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14.
This paper concerns with the ultimate boundedness problem for impulsive fractional delay differential equations. Based on the impulsive fractional differential inequality, the boundedness of Mittag-Leffler functions, and the successful construction of suitable Lyapunov functionals, some algebraic criteria are derived for testing the global ultimate boundedness of the equations, and the estimations of the global attractive sets are provided as well. One example is also given to show the effectiveness of the obtained theoretical results. 相似文献
15.
In this paper, we first utilize fractional calculus, the properties of classical and generalized Mittag-Leffler functions to prove the Ulam–Hyers stability of linear fractional differential equations using Laplace transform method. Meanwhile, Ulam–Hyers–Rassias stability result is obtained as a direct corollary. Finally, we apply the same techniques to discuss the Ulam’s type stability of fractional evolution equations, impulsive fractional evolutions equations and Sobolev-type fractional evolution equations. 相似文献
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17.
In this paper, we prove the existence and uniqueness of solutions for an anti-periodic boundary value problem of nonlinear impulsive differential equations of fractional order α∈(2,3] by applying some well-known fixed point theorems. Some examples are presented to illustrate the main results. 相似文献
18.
We investigate the boundary value problems for nonlinear fractional impulsive differential equations with p-Laplacian operator. By applying some standard fixed point theorems, we obtain new results on the existence and uniqueness of solutions. Examples are given to show the applicability of our results. 相似文献
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20.
In this paper, we study integral boundary value problems for two classes of nonlinear non-instantaneous impulsive ordinary differential equations. More precisely, one is integer order impulsive model, the other is fractional order impulsive model. By using standard fixed point approach, a series of existence results are presented under different conditions. 相似文献