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Solvability of a three-point fractional nonlinear boundary value problem. (English) Zbl 1256.34003

Summary: We study the fractional boundary value problem

c D 0 + q ut=f(t,u(t)),0<t<1
u0=αu ' 0,u1=βu ' η,

where 1<q<2, α,β and c D 0 + q denotes Caputo’s fractional derivative. Using Banach contraction principle and Leray-Schauder nonlinear alternative, we prove the existence and uniqueness of solutions. Some examples are given to illustrate our results.

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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