On Erdélyi–Kober Quadratic Functional-Integral Equation in Banach Algebra

ABSTRACT

Using the technique of a suitable measure of noncompactness in Banach algebra, we prove an existence theorem for some functional-integral equations in Banach algebra, namely Erdélyi–Kober quadratic functional-integral equation. This equation contains as particular cases a lot of integral equations that appear in many branches of nonlinear analysis and its applications. The obtained result is illustrated by an example.

KEYWORDS:

• Banach algebra
• Erdélyi–Kober fractional integral
• existence
• measure of noncompactness
• nonlinear integral equation

2010 Mathematics Subject Classification:

• 45G05
• 47H08

Acknowledgment

The second author extends his appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia).