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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Explicit-Implicit Methods with Applications to Banach Space Valued Functions in Abstract Fractional Calculus

Explicit iterative methods have been used extensively to generate a sequence approximating a solution of an equation on a Banach space setting.

George A. Anastassiou, Ioannis K. Argyros

Chapter 2. Convergence of Iterative Methods in Abstract Fractional Calculus

We present a semi-local convergence analysis for a class of iterative methods under generalized conditions. Some applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.

George A. Anastassiou, Ioannis K. Argyros

Chapter 3. Equations for Banach Space Valued Functions in Fractional Vector Calculi

The aim of this chapter is to solve equations on Banach space using iterative methods under generalized conditions. The differentiability of the operator involved is not assumed and its domain is not necessarily convex. Several applications are suggested including Banach space valued functions of abstract fractional calculus, where all integrals are of Bochner-type. It follows [5].

George A. Anastassiou, Ioannis K. Argyros

Chapter 4. Iterative Methods in Abstract Fractional Calculus

The goal of this chapter is to present a semi-local convergence analysis for some iterative methods under generalized conditions. The operator is only assumed to be continuous and its domain is open. Applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type. It follows [5].

George A. Anastassiou, Ioannis K. Argyros

Chapter 5. Semi-local Convergence in Right Abstract Fractional Calculus

We provide a semi-local convergence analysis for a class of iterative methods under generalized conditions in order to solve equations in a Banach space setting. Some applications are suggested including Banach space valued functions of right fractional calculus, where all integrals are of Bochner-type. It follows [5].

George A. Anastassiou, Ioannis K. Argyros

Chapter 6. Algorithmic Convergence in Abstract g-Fractional Calculus

The novelty of this chapter is the design of suitable algorithms for solving equations on Banach spaces.

George A. Anastassiou, Ioannis K. Argyros

Chapter 7. Iterative Procedures for Solving Equations in Abstract Fractional Calculus

The objective in this study is to use generalized iterative procedures in order to approximate solutions of an equation on a Banach space setting.

George A. Anastassiou, Ioannis K. Argyros

Chapter 8. Approximate Solutions of Equations in Abstract g-Fractional Calculus

The novelty of this chapter is the design of suitable iterative methods for generating a sequence approximating solutions of equations on Banach spaces.

George A. Anastassiou, Ioannis K. Argyros

Chapter 9. Generating Sequences for Solving in Abstract g-Fractional Calculus

The aim of this chapter is to utilize proper iterative methods for solving equations on Banach spaces.

George A. Anastassiou, Ioannis K. Argyros

Chapter 10. Numerical Optimization and Fractional Invexity

We present some proximal methods with invexity results involving fractional calculus.

George A. Anastassiou, Ioannis K. Argyros
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