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Zbl 1214.34007
Rehman, Mujeeb Ur; Khan, Rahmat Ali
Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations.
(English)
[J] Appl. Math. Lett. 23, No. 9, 1038-1044 (2010). ISSN 0893-9659

The authors investigate the existence and uniqueness of solutions for the multi-point boundary value problem for fractional differential equations of the form $$D_t^\alpha y(t)= f(t,y(t),D_t^\beta y(t)),\,\,t\in (0,1),\tag1$$ $$y(0)=0, \,\,D_t^\beta y(1)-\sum_{i=1}^{m-2}\zeta_iD_t^\beta y(\xi_i)=y_0,\tag2$$ where $1<\alpha\leq 2$, $0<\beta<1$, $0<\xi_i<1,$ $i=1,2,\dots,m-2$, $\xi_i\geq 0$ with $\gamma=\sum_{i=1}^{m-2}\zeta_i\xi_i^{\alpha-\beta-1}<1$ and $D_t^\alpha$ 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.
[Claudio Cuevas (Pernambuco)]
MSC 2000:
*34A08
34B10 Multipoint boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: fractional differential equations; multi-point boundary conditions; existence and uniqueness

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