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
\[ D_t^\alpha y(t)= f(t,y(t),D_t^\beta y(t)),\,\,t\in (0,1),\tag{1} \]
\[ y(0)=0, \,\,D_t^\beta y(1)-\sum_{i=1}^{m-2}\zeta_iD_t^\beta y(\xi_i)=y_0,\tag{2} \]
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.


34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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