Solvability for fractional order boundary value problems at resonance. (English) Zbl 1273.34009

Summary: Using coincidence degree theory, we consider the following boundary value problem for a fractional differential equation
\[ \left\{\begin{aligned} & D^\alpha _{0+}x(t)=f(t,x(t),x^\prime(t),x^{\prime\prime}(t)), \quad t\in[0,1], \\&x(0)=x(1),\\& x^\prime(0)=x^{\prime\prime}(0)=0, \end{aligned}\right. \]
where \(D^\alpha _{0+}\) denotes the Caputo fractional differential operator of order \(\alpha\), \(2 < \alpha \leq 3\). A new result on the existence of solutions is obtained.


34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
Full Text: DOI


[1] doi:10.1016/S0378-4371(99)00503-8 · doi:10.1016/S0378-4371(99)00503-8
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