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Solvability of fractional three-point boundary value problems with nonlinear growth. (English) Zbl 1235.34007

Summary: We consider the following fractional boundary value problem:

D 0+ α u(t)=f(t,u(t),D 0+ α-1 u(t)),0<t<1,u(0)=0,u(1)=σu(η),

where 1<α2 is a real number, D 0+ α is the standard Riemann-Liouville derivative, f:[0,1]× 2 is continuous and σ(0,), η(0,1) are given constants such that ση α-1 =1.

By using the coincidence degree theory, we present an existence result at the resonance case.

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