FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The topics covered encompass crucial aspects of the theory, such as well-posedness, regularity, approximation, and optimal control. The book delves into the intricacies of fractional Navier–Stokes equations, fractional Rayleigh–Stokes equations, fractional Fokker–Planck equations, and fractional Schrödinger equations, providing a thorough exploration of these subjects. Numerous real-world applications associated with these equations are meticulously examined, enhancing the practical relevance of the presented concepts.

The content in this monograph is based on the research works carried out by the author and other excellent experts during the past five years. Rooted in the latest advancements, it not only serves as a valuable resource for understanding the theoretical foundations but also lays the groundwork for delving deeper into the subject and navigating the extensive research landscape. Geared towards researchers, graduate students, and PhD scholars specializing in differential equations, applied analysis, and related research domains, this monograph facilitates a nuanced understanding of time-fractional partial differential equations and their broader implications.

Contents:

• Preface
• About the Author
• Introduction
• Preliminaries
• Fractional Navier–Stokes Equations
• Fractional Rayleigh–Stokes Equations
• Fractional Fokker–Planck Equations
• Fractional Schrödinger Equations
• Bibliography
• Index

Readership: Mathematicians and graduate students for research, seminars, and advanced graduate courses in pure and applied mathematics. The researchers using fractional calculus as a tool in the fields of physics, mechanics, engineering, biology, and graduate students for research, seminars, and advanced graduate courses, in physics, mechanics, engineering, biology, and related disciplines.

Key Features:

• There were very few books in the literature presenting systematically the theory of fractional partial differential equations so far
• This book provides a broad scenario of the theory of fractional PDEs and complements the existing literature in fractional calculus
• The author provides the necessary background material required to go further into the subject and explore the rich research literature
• The materials in this book are based on the recent research work done so far by the author and other experts. The contents of the book are systematic and rich