Positive Solutions for a Fractional Differential Equation with Sequential Derivatives and Nonlocal Boundary Conditions

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 of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional deri...

Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary condition D 0 u t a t f t, u t 0, 0 < t < 1, u 0 0, u 1 ∑∞ i 1αiu ξi is considered, where 1 < α ≤ 2 is a real number, D 0 is the standard Riemann-Liouville differentiation, and ξi ∈ 0, 1 , αi ∈ 0,∞ with ∑∞ i 1αiξ α−1 i < 1, a t ∈ C 0, 1 , 0,∞ , f t, u ∈ C 0, 1 × 0,∞ , 0,∞ .

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.