Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus

✍ Scribed by George A. Anastassiou, Ioannis K. Argyros (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 125
• Series: Studies in Computational Intelligence 649
• Edition: 1
• Category: Library

✦ Synopsis

In this short monograph Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, which involve Caputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators. These are studied for the first time in the literature. The chapters are self-contained and can be read independently. 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 short monograph is suitable for researchers, graduate students, to be used in graduate classes and seminars of the above subjects, also to be in all science and engineering libraries.

✦ Table of Contents

Front Matter....Pages i-xii
Fixed Point Results and Their Applications in Left Multivariate Fractional Calculus....Pages 1-15
Fixed Point Results and Their Applications in Right Multivariate Fractional Calculus....Pages 17-30
Semi-local Convergence of Iterative Procedures and Their Applications in k-Multivariate Fractional Calculus....Pages 31-50
Newton-Like Procedures and Their Applications in Multivariate Fractional Calculus....Pages 51-62
Implicit Iterative Algorithms and Their Applications in Multivariate Calculus....Pages 63-70
Monotone Convergence of Iterative Schemes and Their Applications in Fractional Calculus....Pages 71-81
Extending the Convergence Domain of Newton’s Method....Pages 83-92
The Left Multidimensional Riemann–Liouville Fractional Integral....Pages 93-103
The Right Multidimensional Riemann–Liouville Fractional Integral....Pages 105-116

✦ Subjects

Computational Intelligence; Artificial Intelligence (incl. Robotics); Computational Science and Engineering; Complexity