Existence Results for Singular Boundary Value Problem of Nonlinear Fractional Differential Equation

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.

Existence Results for Singular Boundary Value Problem of Nonlinear Fractional Differential Equation

and Applied Analysis 3 where n − 1 ≤ α < n, provided that the right-hand side is pointwise defined on 0,∞ . Definition 2.3. By a solution of the boundary value problem 1.1 we understand a function u ∈ C 0, 1 such thatD 0 u is continuous on 0, 1 and u satisfies 1.1 . Lemma 2.4 see 3 . Assume that u ∈ C 0, 1 ∩ L 0, 1 with a fractional derivative of order α > 0 that belongs to C 0, 1 ∩ L 0, 1 . Th...

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.

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, ...

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