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


  • 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




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


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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How to Cite

Wagdy G. El-Sayed, Mahmoud M. El-Borai, Mohamed M.A. metwali, & Nagwa I. Shemais. (2020). On the existence of continuous solutions of a nonlinear quadratic fractional integral equation. JOURNAL OF ADVANCES IN MATHEMATICS, 19, 14–25. https://doi.org/10.24297/jam.v19i.8802