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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.

MSC:

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

[1] doi:10.1016/S0378-4371(99)00503-8 · doi:10.1016/S0378-4371(99)00503-8
[2] doi:10.1103/PhysRevB.12.2455 · doi:10.1103/PhysRevB.12.2455
[3] doi:10.1016/0888-3270(91)90016-X · doi:10.1016/0888-3270(91)90016-X
[4] doi:10.1016/S0006-3495(95)80157-8 · doi:10.1016/S0006-3495(95)80157-8
[5] doi:10.1063/1.470346 · doi:10.1063/1.470346
[6] doi:10.1016/j.jmaa.2005.02.052 · Zbl 1079.34048 · doi:10.1016/j.jmaa.2005.02.052
[7] doi:10.1016/j.amc.2006.01.007 · Zbl 1102.65136 · doi:10.1016/j.amc.2006.01.007
[8] doi:10.1016/j.na.2009.01.073 · Zbl 1198.26007 · doi:10.1016/j.na.2009.01.073
[9] doi:10.1016/j.na.2009.04.045 · Zbl 1185.26011 · doi:10.1016/j.na.2009.04.045
[10] doi:10.1007/BFb0085076 · doi:10.1007/BFb0085076
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