On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order

In this paper, we present some results on existence of solutions for a quadratic Volterra integral equation of fractional order in two independent variables. This equation is considered in the Banach space of real functions, defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive. An example is provided to illustrate the theory.