On existence and asymptotic behaviour of solutions of a fractional integral equation

Abstract

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions, defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.

Keywords:

• quadratic integral equation
• fractional integral
• existence
• asymptotic behaviour
• measure of non-compactness
• linear modification of the argument
• Schauder fixed point principle

AMS Subject Classsifications::

• 45G10
• 45M99
• 47H09

Acknowledgements

This work was completed when the author was visiting the Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139-4307, USA.