DOI: 10.24193/fpt-ro.2020.1.13

Authors: H.H.G. Hashem and A.M.A. El-Sayed

Abstract: The fractional integration of a function ƒ(t) by a function and some of its properties is presented in [23], [30] and [21]. As an application for this fractional integration we present some existence results for at least one continuous solution for a nonlinear quadratic functional integral equation of fractional (arbitrary) order. Also, some examples and remarks are illustrated. Finally, we prove the existence of maximal and minimal solutions for that equations.

Key Words and Phrases: Quadratic integral equation, Schauder fixed point theorem, continuous solution, maximal and minimal solutions.

2010 Mathematics Subject Classification: 32A55, 11D09, 47H10.

Published on-line: February 1st, 2020.

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