Positive Solutions to n-Order Fractional Differential Equation with Parameter

Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation

and Applied Analysis 3 Definition 2.2 see 12 . The Caputo fractional derivative for a function y : 0,∞ → R can be written as D 0 y t 1 Γ n − α ∫ t 0 t − s n−α−1y n s ds, 2.2 where n α 1, α denotes the integer part of real number α. According to the definitions of fractional calculus, we can obtain that the fractional integral and the Caputo fractional derivative satisfy the following Lemma. Lem...

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

Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.