Fractional Integral Boundary Value Problems Research Articles

Existence results for fractional integral boundary value problem involving fractional derivatives on an infinite interval

In this paper, we study a integral boundary value problem of fractional differential equation with the nonlinearity depending on fractional derivatives of lower order on an infinite interval. We establish a proper compactness criterion in a special function space. By using the Schauder fixed point theorem and Banach contraction mapping principle, we show the existence and uniqueness results of solutions. Two examples are also provided to illustrate the main results. The results obtained generalize and include some known results.

Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions in Banach Spaces

This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multi-orders fractional derivatives and deviating argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space.

Fibre Three-point multi-term fractional integral boundary value problems of fractional functional differential equations with delay

Fibre Three-point multi-term fractional integral boundary value problems of fractional functional differential equations with delay

Existence of positive solutions for a high order fractional differential equation integral boundary value problem with changing sign nonlinearity

In this paper, we investigate the existence of positive solutions for a class of high order fractional differential equation integral boundary value problems with changing sign nonlinearity. By applying cone expansion and cone compression fixed point theorem, we have obtained and proved theorems related to the existence of positive solutions, which highlight the influences of the parameters in different ranges on the existence of positive solutions. Finally, we also give some examples to illustrate our main results.

Explicit iteration to Hadamard fractional integro-differential equations on infinite domain

This paper investigates the existence of the unique solution for a Hadamard fractional integral boundary value problem of a Hadamard fractional integro-differential equation with the monotone iterative technique. Two examples to illustrate our result are given.

Existence of solutions for fractional integral boundary value problems with p(t) -Laplacian operator

Existence of solutions for fractional integral boundary value problems with p(t) -Laplacian operator

Existence and nonexistence of positive solutions for fractional integral boundary value problem with two disturbance parameters

In this paper, we consider a class of fractional differential equations with integral boundary conditions which involve two disturbance parameters. By using the Guo-Krasnoselskii fixed point theorem, new results on the existence and nonexistence of positive solutions for the boundary value problem are obtained. And the impact of the disturbance parameters on the existence of positive solutions is also investigated. Finally, we give some examples to illustrate our main results.

Explicit iteration and unbounded solutions for fractional integral boundary value problem on an infinite interval

By employing the monotone iterative technique, we not only establish the existence of the unique solution for a fractional integral boundary value problem on semi-infinite intervals, but also develop an explicit iterative sequence for approximating the solution and give an error estimate for the approximation, which is an important improvement of existing results.

On Hadamard fractional integro-differential boundary value problems

In this paper, we study the existence and uniqueness of solutions for a fractional integral boundary value problem involving Hadamard type fractional differential equations and integral boundary conditions. Our results are new in the present configuration and are based on some classical ideas of fixed point theory. The paper concludes with some illustrative examples.

A study of Riemann-Liouville fractional nonlocal integral boundary value problems

In this paper, we discuss the existence and uniqueness of solutions for a Riemann-Liouville type fractional differential equation with nonlocal four-point Riemann-Liouville fractional-integral boundary conditions by means of classical fixed point theorems. An illustration of main results is also presented with the aid of some examples. MSC:34A08, 34B10, 34B15.

Positive solutions for a system of fractional integral boundary value problem

In this paper, we shall discuss the existence of positive solutions for the system of fractional integral boundary value problem { D 0 + α u i ( t ) + f i ( t , u 1 ( t ) , u 2 ( t ) ) = 0 , 0 < t < 1 , i = 1 , 2 , u i ( 0 ) = u i ′ ( 0 ) = 0 , u i ( 1 ) = ∫ 0 1 u i ( t ) d η ( t ) , where α∈(2,3] is a real number, D 0 + α is the standard Riemann-Liouville fractional derivative of order α and f i ∈C([0,1]× R + × R + ,R), i=1,2. ∫ 0 1 u i (t)dη(t) denotes the Riemann-Stieltjes integral, i.e., η(t) has bounded variation. By virtue of some inequalities associated with Green’s function, without the assumption of the nonnegativity of f i , we utilize the fixed point index theory to establish our main results. In addition, a square function and its inverse function are used to characterize coupling behaviors of f i , so that f i are allowed to grow superlinearly and sublinearly.MSC: 34B10, 34B18, 34A34, 45G15, 45M20.