Existence, attractiveness and stability of solutions for quadratic Urysohn fractional integral equations

In this paper, existence and attractiveness of solutions for quadratic Urysohn fractional integral equations on an unbounded interval are obtained by virtue of Tichonov fixed point theorem and suitable conjunction of the well known measure ω₀(X) and the spaces C(R⁺). Further, three certain solutions sets X_L,γ, X_1,α and X_{1,(1−(α+v))}, which tending to zero at an appropriate rate t^−ν (ν > 0), ν = γ (or α or 1 − (α + v)) as t → ∞, are introduced and stability of solutions for quadratic Urysohn fractional integral equations are obtained based on these solutions sets respectively by applying Schauder fixed point theorem via some easy checked conditions. An example is given to illustrate the results.