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The existence of solutions to boundary value problems of fractional differential equations at resonance. (English) Zbl 1236.34006

The author obtains a solution of the Riemann-Liouville fractional differential equation

D 0+ α u(t)=f(t,u(t),D 0+ α-1 u(t))a·e·t(0,1)

satisfying the non-local conditions

u(0)=0,D 0+ α-1 u(0)= i=1 m a i D 0+ α-1 u(ξ i ),D 0+ α-2 u(1)= i=1 n b i D 0+ α-2 u(η i )·

It is assumed that 2<α<3, 0<ξ 1 <<ξ m <1, 0<η 1 <<η n <1, i=1 m a i =1, and i=1 n b i η i =1. The existence of a solution at resonance follows from the coincidence degree theorem of Mawhin.

MSC:
34A08Fractional differential equations
34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
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