Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus

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.

Presents recent original research of the authors in Numerical Analysis and Fractional Calculus The chapters are self-contained and can be read independently including an extensive list of references per chapter Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, involvingCaputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators Includes supplementary material: sn.pub/extras

Inhalt
Fixed Point Results and Applications in Left Multivariate Fractional Calculus.- Fixed Point Results and Applications in Right Multivariate Fractional Calculus.- Semi-local Iterative Procedures and Applications In K-Multivariate Fractional Calculus.- Newton-like Procedures and Applications in Multivariate Fractional Calculus.- Implicit Iterative Algorithms and Applications in Multivariate Calculus.- Monotone Iterative Schemes and Applications in Fractional Calculus.- Extending the Convergence Domain of Newton's Method.- The Left Multidimensional Riemann-Liouville Fractional Integral.- The Right Multidimensional Riemann-Liouville Fractional Integral.<p