Positive solutions for a fractional boundary value problem via a mixed monotone operator

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 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.

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 a fractional boundary value problem

Fractional differential equations are a natural generalization of ordinary differential equations. In the last few decades many authors pointed out that differential equations of fractional order are suitable for the metallization of various physical phenomena and that they have numerous applications in viscoelasticity, electrochemistry, control and electromagnetic, and so forth, see 1–4 . This...