共查询到20条相似文献,搜索用时 687 毫秒
1.
Some results on the existence and uniqueness of mild solution for a system of semilinear impulsive differential equations with infinite fractional Brownian motions are proved. The approach is based on Perov's fixed point theorem and a new version of Schaefer's fixed point theorem in generalized Banach spaces. The relationship between mild and weak solutions and the exponential stability of mild solutions are investigated as well. The abstract theory is illustrated with an example. 相似文献
2.
On positive solutions to fractional sum boundary value problems for nonlinear fractional difference equations
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Jiraporn Reunsumrit Thanin Sitthiwirattham 《Mathematical Methods in the Applied Sciences》2016,39(10):2737-2751
In this paper, we study a new class of 3‐point boundary value problems of nonlinear fractional difference equations. Our problems contain difference and fractional sum boundary conditions. Existence and uniqueness of solutions are proved by using the Banach fixed‐point theorem, and existence of the positive solutions is proved by using the Krasnoselskii's fixed‐point theorem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
3.
4.
This paper is concerned with a nonlinear fractional boundary value problem on a star graph. By using a transformation, the suggested problem is converted into an equivalent system of fractional boundary value problem. Schaefer's fixed point theorem and Banach's contraction principle is used to establish its existence and uniqueness results. Further, different kinds of Ulam's type stability results for the proposed problem have been discussed. Finally, two examples are presented to illustrate the application of the obtained results. 相似文献
5.
This paper examines the existence and uniqueness of solutions for the fractional boundary value problems with integral boundary conditions. Banach’s contraction mapping principle and Schaefer’s fixed point theorem have been used besides topological technique of approximate solutions. An example is propounded to uphold our results. 相似文献
6.
Kerboua Mourad 《随机分析与应用》2018,36(2):209-223
In this paper, the approximate controllability for Sobolev-type fractional neutral stochastic evolution equations with fractional stochastic nonlocal conditions and fractional Brownian motion in a Hilbert space are studied. The results are obtained by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem, and methods adopted directly from deterministic control problems for the main results. Finally, an example is given to illustrate the application of our result. 相似文献
7.
刘玉记 《数学年刊A辑(中文版)》2018,39(3):309-330
将具有脉冲的分数阶Bagley-Torvik微分方程边值问题巧妙地转化为积分方程,定义加权Banach空间及全连续算子,运用不动点定理获得该边值问题解的存在性定理.举例说明了定理的应用.最后提出有趣的研究问题. 相似文献
8.
This paper addressed the controllability of nonlinear fractional order integrodifferential systems with input delay. Firstly, the Caputo fractional derivatives and the Mittag‐Leffler functions are employed. Thereafter, we establish a set of sufficient and necessary conditions for the controllability of the linear fractional system. Furtherly, controllability conditions of the nonlinear integrodifferential fractional order system with input delay are acquired by utilizing Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. Finally, an example is presented to demonstrate our main results. 相似文献
9.
By the definition of the higher-order fractional derivative, we explore the central properties of the higher-order Caputo-Fabrizio fractional derivative and integral with a weighted term. Furthermore, by dint of Schaefer''s fixed point theorem, $\alpha$-$\psi$-Contraction theorem, etc., we establish the existence of solutions for nonlinear equations. We also give three examples to make our main conclusion clear. 相似文献
10.
Hossein Fazli HongGuang Sun Juan J. Nieto 《Mathematical Methods in the Applied Sciences》2022,45(1):197-205
We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy-type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well-known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory. 相似文献
11.
We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α ∈ (n-1,n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder's inequality, a suitable singular Gronwall's inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results. 相似文献
12.
Boundary value problems of singular multi‐term fractional differential equations with impulse effects
下载免费PDF全文
![点击此处可从《Mathematische Nachrichten》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Yuji Liu 《Mathematische Nachrichten》2016,289(11-12):1526-1547
We study a class of boundary value problems for nonlinear impulsive fractional differential equations. A weighted function Banach space and a completely continuous nonlinear operator are constructed firstly. Some existence results for solutions of these problems are established continuously. Our analysis relies on the well known Schauder's fixed point theorem. Examples are given to illustrate the main results finally. 相似文献
13.
研究了含积分边界条件的分数阶微分方程的边值问题,首先给出格林函数及性质,其次将问题转化为一个等价的积分方程,最后应用Krasnoselkii及Leggett-Williams不动点定理得到了一个及多个正解的存在性,推广了以往的结果. 相似文献
14.
《Journal of Mathematical Analysis and Applications》1987,122(2):393-407
We provide some new Caratheodory-type selection theorems, i.e., selections for correspondences of two variables which are continuous with respect to one variable and measurable with respect to the other. These results generalize simultaneously Michael's [21]continuous selection theorem for lower-semicontinuous correspondences as well as a Caratheodory-type selection theorem of Fryszkowski [10]. Random fixed point theorems (which generalize ordinary fixed point theorems, e.g., Browder's [6]) follow as easy corollaries of our results. 相似文献
15.
On the controllability of fractional neutral integrodifferential delay equations with nonlocal conditions
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
N. Valliammal C. Ravichandran Ju H. Park 《Mathematical Methods in the Applied Sciences》2017,40(14):5044-5055
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. 相似文献
16.
研究Banach空间中一类非线性分数阶微分方程边值问题.构建此类方程的Green函数,利用非紧测度和相关的不动点定理,得到了此类方程的mild解存在的几个充分条件,所得结果改进和推广了一些已有的结论. 相似文献
17.
C. B. Garcia 《Mathematical Programming》1975,9(1):227-239
Poincaré's last theorem is the most famous among those theorems which are not subsumed by the Lefschetz fixed point theorem. A fixed point theorem is proved directly and constructively which in a special case reduces to the last theorem of Poincaré. 相似文献
18.
Existence and Uniqueness of Solutions for the Initial Value Problem of Fractional $q_{k}$-Difference Equations for Impulsive with Varying Orders
下载免费PDF全文
![点击此处可从《Journal of Nonlinear Modeling and Analysis》网站下载免费的PDF全文](/ch/ext_images/free.gif)
The paper studies the existence and uniqueness for impulsive fractional $q_{k}$-difference equations of initial value problems involving Riemann-Liouville fractional $q_{k}$-integral and $q_{k}$-derivative by defining a new $q$-shifting operator. In this paper, we obtain existence and uniqueness results for impulsive fractional $q_{k}$-difference equations of initial value problems by using the Schaefer''s fixed point theorem and Banach contraction mapping principle. In addition, the main result is illustrated with the aid of several examples. 相似文献
19.
In this paper, by using Kranoselskii fixed point point theorem and Mawhin''s continuation theorem, we establish two existence theorem on the periodic solutions for a class of three-order neutral differential equations. 相似文献
20.
Positive homoclinic solutions of n‐th order difference equations with sign‐changing Green's function
《Mathematical Methods in the Applied Sciences》2018,41(12):4763-4775
In this paper we, consider an n‐th order nonlinear difference equation with parameter dependence. An exhaustive study of the related Green's function is done. The exact expression of the function is given. The range of parameter for which either it has constant sign or it changes sign is obtained. Some existence results for the nonlinear problem are deduced by using the classical Krasnosel'skii's fixed point theorem on cones and fixed point index theory. 相似文献