×

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.

MSC:

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