Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra

Volume 14, Issue 4, pp 181--195 http://dx.doi.org/10.22436/jnsa.014.04.01

Publication Date: November 26, 2020 Submission Date: June 12, 2020 Revision Date: October 18, 2020 Accteptance Date: October 22, 2020

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Authors

Sh. M. Al-Issa - Department of Mathematics, faculty of Art and Science, Lebanese International University, Beirut, Lebanon. - Department of Mathematics, faculty of Art and Science, Lebanese International University, Saida, Lebanon. N. M. Mawed - Department of Mathematics, faculty of Art and Science, Lebanese International University, Saida, Lebanon.

Abstract

Here, we investigate the existence result for a nonlinear quadratic functional integral equation of fractional order using a fixed point theorem of Dhage. The continuous dependence of solution on the delay functions will be studied. As an application, an existence theorem for the fractional hybrid differential equations is proved. Also, we study a general quadratic integral equation of fractional order.

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Keywords

• Dhage fixed point theorem
• continuous dependence of solutions
• hybrid differential equations
• general quadratic integral equation

MSC

•  26A33
•  45D05
•  34A99

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