Fractional Differential Equations: An Approach via Fractional Derivatives

This graduate textbook offers a comprehensive introduction to modern mathematical theory on fractional differential equations, focusing on detailed solution theory and regularity theory. It is suitable for graduate students and researchers in applied and computational mathematics.

Format: Hardback
Length: 368 pages
Publication date: 23 July 2021
Publisher: Springer Nature Switzerland AG

This comprehensive graduate textbook offers a thorough and self-contained introduction to modern mathematical theory on fractional differential equations. It delves into both ordinary and partial differential equations, with a strong emphasis on detailed solution theory, particularly in the context of regularity theory under realistic assumptions regarding the problem data. The text encompasses an extensive bibliography, application-driven modeling, comprehensive exercises, and visually appealing graphic illustrations to enhance its comprehensive coverage of the field. It is highly recommended for advanced graduate students and researchers in applied and computational mathematics, particularly in the areas of applied analysis, numerical analysis, and inverse problems.

The book begins by providing a foundational overview of fractional differential equations, including their definition, properties, and applications. It then delves into various solution techniques, such as the method of characteristics, the Adomian decomposition method, and the perturbation theory. The text also discusses the theory of regularity, which plays a crucial role in determining the existence and uniqueness of solutions to fractional differential equations.

Throughout the book, real-world examples and applications are presented to illustrate the theoretical concepts and their practical implications. These examples range from engineering and physics to biology and economics, showcasing the wide-ranging applications of fractional differential equations. The book includes an extensive bibliography that provides further reading for those interested in exploring specific topics in greater detail. Additionally, application-driven modeling is employed to demonstrate the effectiveness of the proposed solutions in real-world scenarios.

To enhance the learning experience, the text includes numerous exercises that cover a wide range of topics. These exercises are designed to test the understanding of the readers and help them apply the theoretical concepts to solve practical problems. Furthermore, graphic illustrations are used to visually represent the mathematical concepts and equations, making the text more accessible and engaging for students.

In conclusion, this graduate textbook provides a comprehensive and up-to-date introduction to modern mathematical theory on fractional differential equations. It is an invaluable resource for advanced graduate students and researchers seeking to deepen their understanding of this field and apply its principles to real-world problems. With its extensive coverage, practical examples, and engaging format, the book is sure to be a valuable addition to any mathematics library.

Weight: 810g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030760427
Edition number: 1st ed. 2021