### On attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation of fractional order

DOI: http://dx.doi.org/10.12775/TMNA.2008.037

#### Abstract

We study the existence of solutions of a nonlinear quadratic Volterra

integral equation of fractional order.

In our considerations we apply the technique of measures of noncompactness

in conjunction with the classical Schauder fixed point principle.

The mentioned equation is considered in the Banach space of real

functions defined, continuous and bounded on an unbounded interval.

We will show that solutions of the investigated integral equation

are locally attractive.

integral equation of fractional order.

In our considerations we apply the technique of measures of noncompactness

in conjunction with the classical Schauder fixed point principle.

The mentioned equation is considered in the Banach space of real

functions defined, continuous and bounded on an unbounded interval.

We will show that solutions of the investigated integral equation

are locally attractive.

#### Keywords

Quadratic integral Volterra equation of fractional order; measure of noncompactness; local attractivity; asymptotic stability

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