Monotone Convergence of Extended Iterative Methods and Fractional Calculus with Applications

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Anastassiou, George A.^a | Argyros, Ioannis K.^{b; *} | Kumar, Sunil^c

Affiliations: [a] Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A. | [b] Department of Mathematical Sciences, Lawton, Cameron University, OK 73505, USA. iargyros@cameron.edu | [c] Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India-831014. skumar.math@nitjsr.ac.in

Correspondence: [*] Address for correspondence: Department of Mathematical Sciences, Lawton, Cameron University, OK 73505, USA

Abstract: We present monotone convergence results for general iterative methods in order to approximate a solution of a nonlinear equation defined on a partially ordered linear topological space. The main novelty of the paper is that the operators appearing in the iterative method are not necessarily linear. This way we expand of the applicability of iterative methods. Some applications are also provided from fractional calculus using Caputo and Canavati type fractional derivatives and other areas.

Keywords: Monotone convergence, partially ordered linear topological space, Fractional Calculus, Caputo and Canavati type fractional derivatives

DOI: 10.3233/FI-2017-1490

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 241-253, 2017