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Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations. (English) Zbl 1214.34007

The authors investigate the existence and uniqueness of solutions for the multi-point boundary value problem for fractional differential equations of the form

D t α y(t)=f(t,y(t),D t β y(t)),t(0,1),(1)
y(0)=0,D t β y(1)- i=1 m-2 ζ i D t β y(ξ i )=y 0 ,(2)

where 1<α2, 0<β<1, 0<ξ i <1, i=1,2,,m-2, ξ i 0 with γ= i=1 m-2 ζ i ξ i α-β-1 <1 and D t α represents the Riemann-Liouville fractional derivative.

The main tool used by the authors is based on fixed point theory. Specifically, they use the contraction mapping principle and the Schauder fixed point theorem.

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