Abstract
In this paper, we discuss the existence of positive solutions of fractional differential equations on the infinite interval (0,+infty). The positive solution of fractional differential equations is gained by using the properties of the Green’s function, Leray–Schauder’s fixed point theorems, and Guo–Krasnosel’skii’s fixed point theorem. As an application, two examples are given to prove our conclusions.
Highlights
1 Introduction In this article, we investigate the positive solutions for fractional differential equations with infinite-point boundary value conditions:
The existence results of positive solutions are gained by using fixed point theorems
Lemma 2.8 ([26], Guo–Krasnosel’skii’s fixed point theorem) Let E be a Banach space, P ⊂ E be a cone, 1, 2 be two bounded open sets of E centered at the origin with 1 ⊂ 2
Summary
We investigate the positive solutions for fractional differential equations with infinite-point boundary value conditions:. The existence results of positive solutions are gained by using fixed point theorems. 3, we obtain the positive solutions of BVP (1.1) by using the relevant fixed point theorem. Definition 2.2 ([9]) The Riemann–Liouville fractional derivative of order α > 0 of a function u : R+ → R is given by. Lemma 2.5 ([23], Leray–Schauder fixed point theorem) Let B be a bounded, nonempty, convex, and closed subset of Banach space E, and let F : B → E be a completely continuous operator with F(B) ⊂ B.
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