Momani, Shaher M.; El-Khazali, Reyad On the existence of extremal solutions of fractional integro-differential equations. (English) Zbl 0967.45005 J. Fractional Calc. 18, 87-92 (2000). The authors investigate the existence of extremal (maximal and minimal) solutions of the fractional integro-differential equations of the type: \[ x^{(\alpha)} (t)=f(t,x)+ \int^t_{t_0} K\bigl(t,s,x (s)\bigr)ds, \quad \alpha\in \mathbb{R},\;0<\alpha\leq 1. \] The comparison principle and Ascoli lemma have been used in establishing the main results. Also, a result that involves estimating a function satisfying a fractional integro-differential inequality by the extremal solution of the corresponding equation, is obtained. Reviewer: V.Lakshmikantham (Melbourne/Florida) Cited in 2 Documents MSC: 45J05 Integro-ordinary differential equations 45G10 Other nonlinear integral equations 26A33 Fractional derivatives and integrals Keywords:extremal solutions; fractional integro-differential equations; existence PDFBibTeX XMLCite \textit{S. M. Momani} and \textit{R. El-Khazali}, J. Fractional Calc. 18, 87--92 (2000; Zbl 0967.45005)