On the existence of continuous solutions of a nonlinear quadratic fractional integral equation

Wagdy G. El-Sayed; Mahmoud M. El-Borai; Mohamed M.A. metwali; Nagwa I. Shemais

doi:10.24297/jam.v19i.8802

Authors

Wagdy G. El-Sayed Faculty of Science, Alexandria University, Alexandria, Egypt https://orcid.org/0000-0003-3527-0206
Mahmoud M. El-Borai Faculty of Science, Alexandria University, Alexandria, Egypt
Mohamed M.A. metwali Department of mathematics, Faculty of Science , Damanhour Universty, Egypt
Nagwa I. Shemais Department of mathematics, Faculty of Science , Damanhour Universty, Egypt

DOI:

https://doi.org/10.24297/jam.v19i.8802

Keywords:

fractional calculus, Darbo’s fixed point theorem, measure of noncompactnes, Quadratic integral equation

Abstract

We prove an existence theorem for a nonlinear quadratic integral equation of fractional order, in the Banach space of real functions defined and continuous on a closed interval. This equation contains as a special case numerous integral equation studied by other authors. Finally, we give an example for indicating the natural realizations of our abstract result presented in this paper.

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