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 XL,γ, X1,α and X1,(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.

► Two nonlinear quadratic Urysohn fractional integral equations are studied.
► Existence and locally attractive results of solutions for a nonlinear quadratic Urysohn fractional integral equation on an unbounded interval are proved.
► Some interesting stability results of solutions for another quadratic Urysohn fractional integral equation in three certain sets are presented.