Abstract
In this paper, we consider a class of fractional Langevin equations with integral and anti-periodic boundary conditions. By using some fixed point theorems and the Leray–Schauder degree theory, several new existence results of solutions are obtained.
Highlights
We consider the existence of solutions for the following fractional Langevin equation with integral and anti-periodic conditions:
There are a lot of good research results on boundary value problems of fractional differential equations [4–24]
Fractional Langevin equations have been studied by some scholars
Summary
We consider the existence of solutions for the following fractional Langevin equation with integral and anti-periodic conditions:. There are a lot of good research results on boundary value problems of fractional differential equations [4–24]. In [28], via fixed point theorems, Ahmad et al discussed the existence of solutions for fractional Langevin equations with three-point nonlocal boundary value conditions. In [29], Li et al investigated the infinite-point boundary value problem of fractional Langevin equations. For fractional Langevin equation, the boundary value problem with integral and anti-periodic boundary conditions is rarely studied, so the research of this paper is new. 3, we adopt some fixed point theorems and the Leray–Schauder degree theory to obtain the existence of solutions for boundary value problem (1).
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