A Unified Convergence Analysis for Some Iterative Algorithms with Applications to Fractional Calculus
We present a local as well as a semilocal convergence analysis for some iterative algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the application part of the study, we present applications to fractional calculus by using some choices of the operators involving the left and right Caputo derivative, where the operators satisfy the convergence conditions.
International Journal of Applied and Computational Mathematics
Anastassiou, G., & Argyros, I. (2017). A Unified Convergence Analysis for Some Iterative Algorithms with Applications to Fractional Calculus. International Journal of Applied and Computational Mathematics, 3 (2), 323-332. https://doi.org/10.1007/s40819-016-0137-z