A non-local problem for a differential equation of fractional order. (English) Zbl 1314.34023
Summary: We discuss the existence and uniqueness of a solution to the non-local problem for a fractional differential equation
\[
\begin{gathered} D^\alpha_{0^+} u(t)= f(t, u(t)),\qquad\text{a.e. in }(0,1),\\ I^{1-\alpha}_{0^+} u(0)=\beta I^{1-\alpha}_{c^+}u(\xi),\end{gathered}
\]
using the contraction principle and a continuation method.
MSC:
34A08 | Fractional ordinary differential equations |
34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |