Ahmad, Bashir; Sivasundaram, S. Some existence results for fractional integro-differential equations with nonlinear conditions. (English) Zbl 1179.45009 Commun. Appl. Anal. 12, No. 2, 107-112 (2008). 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. Cited in 29 Documents MSC: 45J05 Integro-ordinary differential equations 26A33 Fractional derivatives and integrals 45G10 Other nonlinear integral equations Keywords:Banach space; fractional integro-differential equations; contraction principle; Krasnoselskii’s fixed point theorem PDFBibTeX XMLCite \textit{B. Ahmad} and \textit{S. Sivasundaram}, Commun. Appl. Anal. 12, No. 2, 107--112 (2008; Zbl 1179.45009)