具有分数导数的p-Laplace方程非局部边值问题的多个正解

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.     

Multiple Positive Solutions of Nonlocal Boundary Value Problems for p-Laplacian Equations with Fractional Derivative

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.     

非线性分数阶微分方程Robin型边值问题

In this paper,the existence and multiplicity of positive solutions for Robin type boundary value problem of differential equation involving the Riemann-Liouville fractional order derivative are established.     

On Conformable Delta Fractional Derivative on Time Scales

In this paper, we introduce and investigate the concept of conformable delta fractional derivative on time scales. By using the theory of time scales, we obtain some basic properties of the conformable delta fractional derivative. Our results extend and improve both the results in [9] and the usual delta derivative.     

Existence and Uniqueness of Positive Solutions for a System of Multi-order Fractional Differential Equations

In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of fractional differential equa-tions. Our results are based on the fixed point theorems of increasing operator and the cone theory, some illustrative examples are also presented.     

THREE POSITIVE SOLUTIONS TO BVP FOR p-LAPLACIAN IMPULSIVE FUNCTIONAL DYNAMIC EQUATIONS ON A TIME SCALE

In this paper, we axe interested in the existence of three positive solutions to a BVP for p-Laplacian impulsive functional dynamic equations on a time scale. Using the five-functional fixed theory, we establish a Banach space and an appropriate operator. In this paper, we combine the delta-nabla p-Laplacian BVP with impulsive functional dynamic equations, and obtain some new sufficient conditions for the existence of three positive solutions to the BVP, and our result here generalizes the previous related results.     

ON DISCRETE SEQUENTIAL FRACTIONAL BOUNDARY VALUE PROBLEM WITH FRACTIONAL BOUNDARY CONDITIONS

In this paper we consider a discrete fractional boundary value problem(FBVP for short). We provide a delicate analysis for the property of Green’s function. Our analysis motivates the study of discrete fractional boundary value problems with fractional boundary conditions. As an application, we give conditions under which such problems admit at least one positive solution. Our results extend the results presented in [4].     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel'skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.     

Analysis of an Implicit Finite Difference Scheme for Time Fractional Diffusion Equation

Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈(0, 1). In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper.     

A Positive Solution of Mixed Non-Linear Fractional Delay Differential Equations with Integral Boundary Conditions

In this paper, we study mixed non-linear fractional delay differential equations with integral boundary conditions. We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind. Further, we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii’s fixed point theorem and Banach contraction principle.     

半正的分数阶微分方程(n-1,1)-型积分边值问题的多个正解

采用Riemann-Liouville分数阶导数,研究了半正的分数阶微分方程(n-1,1)-型积分边值问题,获得了参数λ的一个区间,使得λ落在这个区间的时候,该半正的分数阶微分方程边值问题有多个正解.     

分数阶微分方程的一些新结果

第一部分,介绍分数阶导数的定义和著名的Mittag—Leffler函数的性质．第二部分,利用单调迭代方法给出了具有2序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性和唯一性．第三部分,利用上下解方法和Schauder不动点定理给出了具有2序列Riemann—Liouville分数阶导数微分方程周期边值问题解的存在性．第四部分,利用Leray—Schauder不动点定理和Banach压缩映像原理建立了具有n序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性、唯一性和解对初值的连续依赖性．第五部分,利用锥上的不动点定理给出了具有Caputo分数阶导数微分方程边值问题,在超线性（次线性）条件下C310,11正解存在的充分必要条件．最后一部分,通过建立比较定理和利用单调迭代方法给出了具有Caputo分数阶导数脉冲微分方程周期边值问题最大解和最小解的存在性．     

Nonlocal boundary value problem for fractional differential equations with p‐Laplacian

In this paper, we are concerned with the existence of positive solutions for the following nonlocal BVP of fractional DEs with p‐Laplacian operator By using the fixed point theorem in a cone, multiplicity solutions of the BVP are obtained. An example is also given to show the effectiveness of the obtained result. Copyright © 2013 John Wiley & Sons, Ltd.     

Caputo–Hadamard Fractional Derivatives of Variable Order

In this article, we present three types of Caputo–Hadamard derivatives of variable fractional order and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is obtained and an estimation for the error is given. At the end, we compare the exact fractional derivative of a concrete example with some numerical approximations.     

带有临界增长的分数阶Kirchhoff方程的半经典解

本文研究如下带有临界增长的分数阶Kirchhoff方程ε2sM(ε2s-3∫∫R3×R3- |u(x)-u(y)|2/(x-y|3+2s|2dxdy)(-△)su+V(x)u = λW(x)f(u)+K(x)|u|2*s-2u,x ∈ R3,其中 M 是一个连续正的Kirchhoff函数,A＞0是一个参数,3/4 ＜ ...     

Infinitely Many Solutions for Schr?dinger–Choquard–Kirchhoff Equations Involving the Fractional p-Laplacian

In this article,we show the existence of infinitely many solutions for the fractional pLaplacian equations of Schr?dinger-Kirchhoff type equation ■ ,where(-△)_p~s is the fractional p-Laplacian operator,[u]_(s,p) is the Gagliardo p-seminorm,0 s 1 q p N/s,α∈(0,N),M and V are continuous and positive functions,and k(x) is a non-negative function in an appropriate Lebesgue space.Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of the symmetric mountain pass lemma,we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters λ and β.     

Non-existence for fractionally damped fractional differential problems

In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part.     

A general study on random integro-differential equations of arbitrary order

Here the broad study is depending on random integro-differential equations (RIDE) of arbitrary order. The fractional order is in terms of $\psi$-Hilfer fractional operator. This work reveals the dynamical behaviour such as existence, uniqueness and stability solutions for RIDE involving fractional order. Thus initial value problem (IVP), boundary value problem (BVP), impulsive effect and nonlocal conditions are taken in account to prove the results.