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Monotonic solutions of functional integral and differential equations of fractional order. (English) Zbl 1181.45016

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.

MSC:

45G10 Other nonlinear integral equations
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
26A33 Fractional derivatives and integrals
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