Abstract
In this paper, we are concerned with the following fractional equation: with the boundary value conditions where is the standard Caputo derivative with and δ, γ are constants with , . By applying a new fixed point theorem on cone and Krasnoselskii’s fixed point theorem, some existence results of positive solution are obtained. MSC: 34A08, 34B15, 34B18.
Highlights
1 Introduction In this paper, we are concerned with the existence of positive solutions for the fractional equation
There has been a significant development in the study of fractional differential equations and inclusions in recent years, see the monographs of Podlubny [ ], Kilbas et al [ ], Lakshmikantham et al [ ], Samko et al [ ], Diethelm [ ], and the survey by Agarwal et al [ ]
Owing to its importance in physics, the existence of solutions to this problem has been studied by many authors; see, for example, [ – ] and references therein
Summary
We are concerned with the existence of positive solutions for the fractional equation. There have been a few papers dealing with the existence of solutions for fractional equations of order α ∈ In [ ], Liang and Zhang studied the following nonlinear fractional boundary value problem: Dα +u(t) = f t, u(t) , t ∈ ( , ), u( ) = u ( ) = u ( ) = u ( ) = , where < α ≤ , f (t, u) ∈ C([ , ] × [ , ∞), [ , ∞)) is nondecreasing relative to u, Dα + is the Riemann-Liouville fractional derivative of order α.
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