Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

Positive solutions for a class of fractional differential coupled system with integral boundary value conditions

This paper investigates the existence of positive solutions for the following high-order nonlinear fractional differential boundary value problem (BVP, for short)  Dα 0+u(t) + f(t, v(t)) = 0, t ∈ (0, 1), Dα 0+v(t) + g(t, u(t)) = 0, t ∈ (0, 1), u(j)(0) = v(j)(0) = 0, 0 ≤ j ≤ n− 1, j 6= 1, u′(1) = λ ∫ 1 0 u(t)dt, v′(1) = λ ∫ 1 0 v(t)dt, where n − 1 < α ≤ n, n ≥ 3, 0 ≤ λ < 2, Dα 0+ is the ...

Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations

In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equations Du(t) + λf(t, u(t), v(t)) = 0, Dv(t) + λg(t, u(t), v(t)) = 0, t ∈ (1, e), λ > 0, u(1) = v(1) = 0, 0 ≤ j ≤ n− 2, u(e) = μ ∫ e 1 v(s) ds s , v(e) = ν ∫ e

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 triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...