Existence and stability results for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes quadratic integral equations

Keywords: Volterra–Stieltjes integral equation Fractional integral–differential equations Riemann–Liouville fractional operators Existence and stability of solutions Fixed point a b s t r a c t Our aim in this paper is to study the existence and the stability of solutions for Riemann–Liouville Volterra–Stieltjes quadratic integral equations of fractional order. Our results are obtained by using some fixed point theorems. Some examples are provided to illustrate the main results. Fractional differential and integral equations have recently been applied in various areas of engineering, mathematics, physics and bio-engineering and other applied sciences. There has been a significant development in ordinary and partial fractional differential and integral equations in recent years; see the monographs of Abbas et al. Recently interesting results of the stability of the solutions of various classes of integral equations of fractional order have obtained by Abbas et al.