Boundary value problems for Bagley--Torvik fractional differential equations at resonance

Svatoslav Stanek;


We investigate the nonlocal fractional boundary value problem $u'' =A^c \kern-2pt D^{\alpha}u+f(t,u,{}^c \kern-2pt D^{\mu}u, u')$, $u'(0)=u'(T)$, $\Lambda(u)=0$, at resonance. Here, $\alpha \in (1,2)$, $\mu \in (0,1)$, $f$ and $\Lambda\colon C[0,T] \to \mathbb{R}$ are continuous. Existence results are proved by the Leray--Schauder degree method.

Vol. 19 (2018), No. 1, pp. 611-623
DOI: 10.18514/MMN.2018.1809

Download: MMN-1809