On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order

Abstract EN

We investigate a class of functional integral equations of fractional order given by x(t)=q(t)+f1(t,x(α1(t)),x(α2(t)))+(f2(t,x(β1(t)),x(β2(t)))/Γ(α))×∫0t(t−s)α−1f3(t,s,x(γ1(s)), x(γ2(s)))ds: sufficient conditions for the existence, global attractivity, and ultimate positivity of solutions of the equations are derived.

The main tools include the techniques of measures of noncompactness and a recent measure theoretic fixed point theorem of Dhage.

Our investigations are placed in the Banach space of continuous and bounded real-valued functions defined on unbounded intervals.

Moreover, two examples are given to illustrate our results.