In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function.
Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book's results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering.As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
Series
Edition
Softcover reprint of the original 1st ed. 2016
Language
Place of publication
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
2 farbige Abbildungen
XVI, 423 p. 2 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 24 mm
Weight
ISBN-13
978-3-319-80003-5 (9783319800035)
DOI
10.1007/978-3-319-26721-0
Schweitzer Classification
George Anastassiou is Professor at the University of Memphis. Research interests include Computational analysis, approximation theory, probability, theory of moments. Professor Anastassiou has authored and edited several publications with Springer including "Fractional Differentiation Inequalities" (c) 2009, "Fuzzy Mathematics: Approximation Theory" (c) 2010, "Intelligent Systems: Approximation by Artificial Neural Networks" (c) 2014, "The History of Approximation Theory" (c) 2005, "Modern Differential Geometry in Gauge Theories" (c) 2006, and more.
Razvan Alex Mezei received his PhD from the University of Memphis and currently holds an assistant professorship and Lenoir-Rhyne University, Hickory, North Carolina. He teaches mathematics as well as computer science/IT courses to undergraduates and is a computing sciences program coordinator. Mezei has extensive experience in computer programming and software development and has written several publications with George Anastassiou.
Newton-Like Methods on Generalized Banach Spaces andFractional Calculus.- Semilocal Convegence of Newton-Like Methods and Fractional Calculus.- Convergence of Iterative Methods and Generalized Fractional Calculus.- Fixed Point Techniques And Generalized Right Fractional Calculus.- Approximating Fixed Points And K-Fractional Calculus.- Iterative Methods And Generalized G-Fractional Calculus.- Unified Convergence Analysis For Iterative
Algorithms And Fractional Calculus.- Convergence Analysis For Extended Iterative Algorithms
And Fractional And Vector Calculus.- Convergence Analysis For Extended Iterative
Algorithms And Fractional Calculus.- Secant-Like Methods And Fractional Calculus.- Secant-Like Methods And Modified G- Fractional Calculus.- Secant-Like Algorithms And Generalized Fractional Calculus.- Secant-Like Methods And Generalized G-Fractional Calculus Of Canavati-Type.- Iterative Algorithms And Left-Right Caputo Fractional Derivatives.- Iterative Methods On Banach Spaces With A
Convergence Structure And Fractional Calculus.- Inexact Gauss-Newton Method For Singular Equations.- The Asymptotic Mesh Independence Principle.- Ball Convergence Of A Sixth Order Iterative Method.- Broyden's Method With Regularily Continuous Divided Differences.- Left General Fractional Monotone Approximation.- Right General Fractional Monotone Approximation Theor.- Left Generalized High Order Fractional Monotone Approximation.- Right Generalized High Order Fractional Monotone Approximation.- Advanced Fractional Taylor's Formulae.- Generalized Canavati Type Fractional Taylor's Formulae.
