A Fractional Order of Convergence Rate for Successive Methods: Examples on Integral Equations

This paper is devoted to investigating the fractional order of con-vergence of operator iteration schemes and, as a means of obtaining rapid convergence, rediscovering fixed-point methods by fractional cal-culus. In addition, a new definition for fractional Gateaux derivative is used which seems a key idea for accelerating the convergence of iterative methods. At the end, the relevance of the theory and applications of integral equations are given