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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.

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