El-Sayed, A. M. A.; Hashem, H. H. G. Monotonic solutions of functional integral and differential equations of fractional order. (English) Zbl 1181.45016 Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 7, 8 p. (2009). Summary: The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equations have been studied earlier. Here we are concerned with a singular quadratic functional integral equation. The existence of positive monotonic solutions \(x \in L_1[0,1]\) is proved. The fractional order nonlinear functional differential equation is given as a special case. Cited in 7 Documents MSC: 45G10 Other nonlinear integral equations 47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. 26A33 Fractional derivatives and integrals Keywords:quadratic functional integral equations; positive monotonic solutions; measure of noncompactness; fractional order integral PDFBibTeX XMLCite \textit{A. M. A. El-Sayed} and \textit{H. H. G. Hashem}, Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 7, 8 p. (2009; Zbl 1181.45016) Full Text: EuDML EMIS