SOLVABILITY OF DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEMS

In this paper, by introducing a new approach, we investigate a discrete fractional boundary value problem. We transform a fractional nonlinear difference equation on a finite discrete segment with boundary conditions into a system, and obtain some conditions for the existence of solutions to the equation, based on coincidence degree theory and matrix theory but not on Green’s function.     

BOUNDARY VALUE METHODS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

This paper deals with the numerical computation and analysis for Caputo fractional differential equations(CFDEs).By combining the p-order boundary value methods(B-VMs)and the m-th Lagrange interpolation,a type of extended BVMs for the CFDEs with y-order(0相似文献   

THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0+ u(t) = f (t, u(t), c D σ 0+ u(t)), t ∈ [0, T ], u(0) = αu(η), u(T ) = βu(η), where 1 < δ < 2, 0 < σ < 1, α, β∈ R, η∈ (0, T ), αη(1 -β) + (1-α)(T βη) = 0 and c D δ 0+ , c D σ 0+ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results.     

ON SOME BOUNDARY VALUE PROBLEMS FOR NONHOMOGENOUS POLYHARMONIC EQUATION WITH BOUNDARY OPERATORS OF FRACTIONAL ORDER

In the paper we study questions about solvability of some boundary value problems for a non-homogenous poly-harmonic equation.As a boundary operator we consider differentiation operator of fractional order in Miller-Ross sense.The considered problem is a generalization of well-known Dirichlet and Neumann problems.     

SOLVABILITY FOR FRACTIONAL MULTI-POINT BOUNDARY VALUE PROBLEMS ON HALF LINE

In this paper,we consider the fractional multi-point boundary value problem. By Leggett-Williams fixed point theorem,sufficient conditions that guarantee the existence of three positive solutions are obtained.     

SOLVABILITY FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION BOUNDARY VALUE PROBLEMS AT RESONANCE

The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.     

A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

In this paper,we discuss the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations.Our main result is based on a hybrid fixed point theorem for a sum of three operators due to Dhage,and is well illustrated with the aid of an example.     

POSITIVE SOLUTION TO A CLASS OF SINGULAR FRACTIONAL BOUNDARY VALUE PROBLEMS

In this paper,we investigate the existence and uniqueness of positive solutions to a class of singular fractional boundary value problem.The existence of positive solutions to the problem is based on a fixed point theorem in partially ordered sets.     

EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo's derivative     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO FRACTIONAL BOUNDARY VALUE PROBLEMS

In this paper, using fixed point theorems of general β-concave operators in ordered Banach space, we obtain the existence and uniqueness of positive solutions to a class of fractional boundary problem. In the end, an example is given to illustrate our main result.     

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.     

两类分数阶微分方程的边值问题

本文研究了两类非线性项含有未知函数导数的分数阶微分方程的边值问题.利用分数阶微积分的性质及Banach不动点定理,获得了解的存在唯一性等有关结果,推广了已有文献的结论.     

EXISTENCE OF SOLUTIONS TO COUPLED FRACTIONAL ORDER SYSTEMS WITH THREE-POINT BOUNDARY CONDITIONS

This paper investigates a class of coupled systems of nonlinear fractional differential equations with three-point boundary conditions. Under suitable conditions the existence of solutions is obtained using the Schauder fixed point theorem.     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETER

In this paper, we consider a class of nonlinear fractional differential equation boun- dary value problem with a parameter. By some fixed point theorems, sufficient con- ditions for the existence, nonexistence and multiplicity of positive solutions to the system are obtained. An example is given to illustrate the main results.     

SOLUTION FOR TWO-POINT BOUNDARY VALUE PROBLEM OF THE SEMILINEAR FRACTIONAL DIFFERENTIAL EQUATION

In this paper, we establish the existence result of solution and positive solution for two-point boundary value problem of a semilinear fractional differential equation by using the Leray-Schauder fixed-point theorem. The discussion is based on the system of integral equations on a bounded region.     

EXISTENCE OF MULTIPLE SOLUTIONS TO A FRACTIONAL DIFFERENCE BOUNDARY VALUE PROBLEM WITH PARAMETER

By establishing the corresponding variational framework, and using critical point theory, we give the existence of multiple solutions to a fractional difference boundary value problem with parameter. Under some suitable assumptions we obtain some results which ensure the existence of well precise interval of parameter for which the problem admits multiple solutions.     

带有p-Laplace算子的分数阶边值问题的特征区间

本文研究了一类带有p-Laplace算子的分数阶微分方程两点边值问题.利用锥上的不动点定理,得到了这类边值问题的特征区间,推广了整数阶边值问题情形的结论.     

EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

In this paper, using the property of the corresponding Green’s function and fixed point index theory, some sufficient conditions for the multiplicity and nonexistence of positive solutions to a class of nonlinear fractional boundary value problem are obtained. Three examples are given to show the effectiveness of our results.     

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.     

POSITIVE SOLUTIONS TO A COUPLED SYSTEM OF FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM WITH DELAY

In this paper, we study the existence of positive solutions to an integral boundary value problem with delay for a coupled system of fractional differential equations. By using the Krasnoselskii fixed point theorem, we obtain sufficient conditions for the existence of at least one or two positive solutions to the problem under some weaker conditions.