Positive solutions for higher-order nonlinear fractional differential equation with integral boundary condition

Positive solutions for higher - order nonlinear fractional differential equation with integral boundary condition ∗

In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary condition. The fractional differential operator here is the Caputo’s fractional derivative. By means of fixed point theorems, the existence and multiplicity results of positive solutions are obtained. Furthermore, some examples given here illustrate that the results are almost sharp.

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Existence and Uniqueness of Positive Solutions to Higher-order Nonlinear Fractional Differential Equation with Integral Boundary Conditions

In this article, we consider the nonlinear fractional order threepoint boundary-value problem D 0+u(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = u′(0) = · · · = u(n−2)(0) = 0, u(n−2)(1) = Z η

Existence of solutions for a nonlinear fractional differential equation with integral boundary condition

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: { D t x(t) = f(t, x(t), D β t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = ∫ 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle. Keywords—Fractional differential equation; Integral boundary condi...