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1.
In this paper,we study the multiple positive solutions of integral boundary value problems for a class of p-Laplacian differential equations involving the Caputo fractional derivative.Using a fixed point theorem due to Avery and Peterson,we obtain the existence of at least three positive decreasing solutions of the nonlocal boundary value problems. We give an example to illustrate our results.  相似文献   

2.
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative Dαo+is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel’skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.  相似文献   

3.
In this paper,we study the multiple positive solutions of integral boundary value problems for a class of p-Laplacian differential equations involving the Caputo fractional derivative.Using a fixed point theorem due to Avery and Peterson,we obtain the existence of at least three positive decreasing solutions of the nonlocal boundary value problems. We give an example to illustrate our results.  相似文献   

4.
In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.  相似文献   

5.
司家芳  蒋威 《数学季刊》2012,(1):117-122
The problem of sliding mode control for fractional differential systems with statedelay is considered.A novel sliding surface is proposed and a controller is designed correspondingly,such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point.And the stability of the proposed control design is discussed.  相似文献   

6.
李旭  王世朋 《数学季刊》2011,(2):217-222
This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p(y''(0),y'''(0))=0,q(y''(1),y'''(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.  相似文献   

7.
毛伟  韩修静  陈波 《数学季刊》2011,(3):405-409
In this paper,we present the semi-implicit Euler(SIE)numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition.  相似文献   

8.
By applying the monotone iterative method,this study develops two explicit monotone iterative sequences for approximating the minimal and maximal positive solutions.At the same time,by applying the Banach fixed-point theory,an explicit iterative sequence and error estimate for approximating the unique positive solution is obtained.Some examples are given to illustrate the application of the results.  相似文献   

9.
This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.  相似文献   

10.
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations {[φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.  相似文献   

11.
In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.  相似文献   

12.
利用Adomian分解法, 得到了由任意阶分数微分描述的具有阻尼特性的黏弹性连续梁的解析解.解中包含了任意的初始条件和零输入.为了更明确的分析, 假定初始条件是奇次的,输入受力是针对某种特定梁的特殊过程.分别考虑了两种简单情况下梁的响应:阶跃激励和脉冲激励.然后在系统的不同组参数条件下绘制了梁的位移图,并且讨论了梁在不同微分阶数下响应情况.  相似文献   

13.
Herein, an approach known as conformable double Laplace decomposition method (CDLDM) is suggested for solving system of non-linear conformable fractional differential equations. The devised scheme is the combination of the conformable double Laplace transform method (CDLTM) and, the Adomian decomposition method (ADM). Obtained results from mathematical experiments are in full agreement with the results obtained by other methods. Furthermore, according to the results obtained we can conclude that the proposed method is efficient, reliable and easy to be implemented on related many problems in real-life science and engineering.  相似文献   

14.
Adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations. Convergence of the method has been discussed with some illustrative examples. In particular, for the initial value problem:
  相似文献   

15.
Series Solutions of Systems of Nonlinear Fractional Differential Equations   总被引:1,自引:0,他引:1  
Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.   相似文献   

16.
We use Adomian decomposition method for solving the fractional nonlinear two-point boundary value problem
where D is Caputo fractional derivative, c is a constant, μ > 0, and F:[0,1]×[0,)→[0,) a continuous function. The fractional Bratu problem is solved as an illustrative example.  相似文献   

17.
Adomian decomposition method has been used to obtain solutions of linear/nonlinear fractional diffusion and wave equations. Some illustrative examples have been presented.  相似文献   

18.
In this paper, we propose a new method called the fractional natural decomposition method (FNDM). We give the proof of new theorems of the FNDM, and we extend the natural transform method to fractional derivatives. We apply the FNDM to construct analytical and approximate solutions of the nonlinear time‐fractional Harry Dym equation and the nonlinear time‐fractional Fisher's equation. The fractional derivatives are described in the Caputo sense. The effectiveness of the FNDM is numerically confirmed. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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