Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical, chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory, as it might have once seemed. The present book seeks to demonstrate this using various examples of equations and models with fractional and generalized operators. Intended for students and researchers in mathematics, physics, chemistry, biology and engineering, it systematically offers a wealth of useful tools for fractional calculus.

Offers a detailed introduction to and advanced theory of fractional calculus Pursues a step-by-step approach to solve related problems Includes material that will be of interest to mathematicians, physicists, chemists, biologists and engineers

Autorentext

Trifce Sandev is a research scientist at the Macedonian Academy of Sciences and Arts and an Assistant Professor of Theoretical Physics at the Faculty of Natural Sciences and Mathematics in Skopje. After completing his PhD in Theoretical Physics in 2012, he was a postdoctoral researcher at the Max Planck Institute for the Physics of Complex Systems in Dresden. Selected for the Presidential Award for Best Young Scientist in Macedonia (2011), his main research interest is in stochastic processes in complex systems.
ivorad Tomovski has held the position of Full Professor at the Institute of Mathematics at Ss. Cyril and Methodius University in Skopje, Macedonia since 2010. He completed his PhD in Approximation Theory and Fourier Analysis in 2000, and has since held visiting researcher positions at many universities and research institutes across Europe. He has published over 100 journal articles and international conference papers in the areasof Pure and Applied Mathematical Sciences.

Zusammenfassung

"In this valuable and interesting book, the authors treat the vast theory of fractional calculus. ... The book is very well-organized and carefully written. The authors listed a plentiful of references in each section, which help the reader for further study. ... Detailed computations and many graphical representations enhance the understanding of the reader. Researchers and students from diverse scientific communities working in fractional calculus will find this book a source of various ideas and tools." (Seunghyeok Kim, zbMATH 1473.35002, 2021)

"The book is written in a very concise and precise mathematical manner. The results concerning different types of fractional equations gathered in the book may be a valuable resource to researchers interested in the modeling of various processes related to anomalous diffusion behavior." (Krzysztof Rogowski, Mathematical Reviews, August, 2021)

"This book is a very specialized text that considers fractional calculus and fractional differential equations used in the study of fractional stochastic and kinetic models. ... The current book is essentially a monograph that explores applications using several variations of the fractional calculus." (MAA Reviews, March 1, 2020)

Inhalt

Introduction: Mittag-Leffler and Other Related Functions.- Generalized Differential and Integral Operators.- Cauchy Type Problems.- Fractional Diffusion and Fokker-Planck Equations.- Fractional Wave Equations.- Generalized Langevin Equation.- Fractional Generalized Langevin Equation.- Appendix A: Completely monotone, Bernstein and Stieltjes Functions.- Appendix B: Tauberian Theorems.