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Some existence results for fractional integro-differential equations with nonlinear conditions. (English) Zbl 1179.45009

Summary: We study some existence and uniqueness results in a Banach space for a fractional integro-differential equation with nonlinear condition
\[ ^cD^qx(t) = f(t,x(t)) + \int^t_0 k(t,s,x(s))\,ds,\;t\in [0,T],\;0 <g< 1,\quad x(0) =x_0-g(x). \]
The contraction mapping principle and Krasnoselskii’s fixed point theorem are employed to establish the results.

MSC:

45J05 Integro-ordinary differential equations
26A33 Fractional derivatives and integrals
45G10 Other nonlinear integral equations
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