Momani, Shaher M. Local and global existence theorems on fractional integro-differential equations. (English) Zbl 0967.45004 J. Fractional Calc. 18, 81-86 (2000). The author obtains local and global existence and uniqueness theorems of the fractional integro-differential equations of the type: \[ x^{(\alpha)} (t)=f(t,x)+ \int^t_{t_0} k\bigl(t,s,x(s) \bigr)ds, \quad \alpha \in \mathbb{R},\;0<\alpha\leq 1, \] as application of Schauder’s and Tykhonov’s fixed-point theorems. Reviewer: V.Lakshmikantham (Melbourne/Florida) Cited in 22 Documents MSC: 45J05 Integro-ordinary differential equations 45G10 Other nonlinear integral equations 26A33 Fractional derivatives and integrals Keywords:existence; fractional integro-differential equations PDFBibTeX XMLCite \textit{S. M. Momani}, J. Fractional Calc. 18, 81--86 (2000; Zbl 0967.45004)