Functional Numerical Methods Applications to Abstract Fractional Calculus 1st Edition by George Anastassiou, Ioannis Argyros 3319695266 9783319695266

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ISBN-10 :  3319695266 

ISBN-13 :  9783319695266

Author:  George A. Anastassiou, Ioannis K. Argyros

This book presents applications of Newton-like and other similar methods to solve abstract functional equations involving fractional derivatives. It focuses on Banach space-valued functions of a real domain – studied for the first time in the literature. Various issues related to the modeling and analysis of fractional order systems continue to grow in popularity, and the book provides a deeper and more formal analysis of selected issues that are relevant to many areas – including decision-making, complex processes, systems modeling and control – and deeply embedded in the fields of engineering, computer science, physics, economics, and the social and life sciences. The book offers a valuable resource for researchers and graduate students, and can also be used as a textbook for seminars on the above-mentioned subjects. All chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references.

Functional Numerical Methods: Applications to Abstract Fractional Calculus 1st Table of contents:

1 Explicit-Implicit Methods with Applications to Banach Space Valued Functions in Abstract Fraction
1.1 Introduction
1.2 Semi-local Convergence for Implicit Methods
1.3 Semi-local Convergence for Explicit Methods
1.4 Applications to X-valued Fractional Calculus
References
2 Convergence of Iterative Methods in Abstract Fractional Calculus
2.1 Introduction
2.2 Semi-local Convergence for Implicit Methods
2.3 Semi-local Convergence for Explicit Methods
2.4 Applications to Abstract Fractional Calculus
References
3 Equations for Banach Space Valued Functions in Fractional Vector Calculi
3.1 Introduction
3.2 Semi-local Convergence for Implicit Methods
3.3 Semi-local Convergence for Explicit Methods
3.4 Applications to X-valued Fractional and Vector Calculi
References
4 Iterative Methods in Abstract Fractional Calculus
4.1 Introduction
4.2 Semi-local Convergence for Implicit Methods
4.3 Semi-local Convergence for Explicit Methods
4.4 Applications to X-valued Fractional Calculus
References
5 Semi-local Convergence in Right Abstract Fractional Calculus
5.1 Introduction
5.2 Semi-local Convergence for Implicit Methods
5.3 Semi-local Convergence for Explicit Methods
5.4 Applications to X-valued Right Fractional Calculus
References
6 Algorithmic Convergence in Abstract g-Fractional Calculus
6.1 Introduction
6.2 Semi-local Convergence Analysis
6.3 Applications to X-valued Modified g-Fractional Calculus
References
7 Iterative Procedures for Solving Equations in Abstract Fractional Calculus
7.1 Introduction
7.2 Semi-local Convergence for Implicit Methods
7.3 Semi-local Convergence for Explicit Methods
7.4 Applications to Abstract Fractional Calculus
References
8 Approximate Solutions of Equations in Abstract g-Fractional Calculus
8.1 Introduction
8.2 Semi-local Convergence Analysis
8.3 Applications to X-valued g-Fractional Calculus
References
9 Generating Sequences for Solving in Abstract g-Fractional Calculus
9.1 Introduction
9.2 Semi-local Convergence Analysis
9.3 Applications to X-valued g-Fractional Calculus of Canavati Type
References
10 Numerical Optimization and Fractional Invexity
10.1 Introduction
10.2 Convergence of Method (10.1.2)
10.3 Multivariate Fractional Derivatives and Invexity

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Tags: Functional, Numerical Methods, Applications, Fractional Calculus, George Anastassiou, Ioannis Argyros