A fixed point technique for some iterative algorithm with applications to generalized right fractional calculus

We present a fixed point technique for some iterative algorithms on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies such as [I. K. Argyros, Approx. Theory Appl., 9 (1993), 1{9], [I. K. Argyros, Southwest J. Pure Appl. Math., 1 (1995), 30-36], [I. K. Argyros, Springer-Verlag Publ., New York, (2008)], [P. W. Meyer, Numer. Funct. Anal. Optim., 9 (1987), 249-259] require that the operator involved is Fréchet-differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of these methods to include right fractional calculus as well as problems from other areas. Some applications include fractional calculus involving right generalized fractional integral and the right Hadamard fractional integral. Fractional calculus is very important for its applications in many applied sciences.