Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions. (English) Zbl 1180.34003

Summary: This paper studies existence and uniqueness results in a Banach space for a two-point boundary value problem involving a nonlinear fractional differential equation given by
\[ {}^cD^qx(t)= f(t,x(t)), \quad 0<t<1,\;1<q\leq 2, \]
\[ \alpha x(0)+\beta x'(0)=\gamma_1, \quad \alpha x(1)+\beta x'(1)=\gamma_2. \]
Our results are based on contraction mapping principle and Krasnoselskii’s fixed point theorem.


34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
26A33 Fractional derivatives and integrals