SPECIAL FUNCTIONS OF FRACTIONAL CALCULUS

This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.

Contents:

• Mathematical Background
• Fox H-Function and Related Functions
• Elements of Random Walk Theory
• CTRW on Combs
• Heterogeneous Diffusion Processes
• Diffusion Processes with Stochastic Resetting
• Random Search
• Diffusion on Fractal Tartan
• Finite-Velocity Diffusion
• Appendices:
  Functional CalculusStochastic Differential EquationsLarge Deviation PrincipleFractals and Fractal DimensionImplementation of Wolfram Mathematica

Readership: Advanced undergraduate and graduate students, researchers in the fields of stochastic processes, fractional calculus, anomalous diffusion, random search, stochastic resetting, econophysics.

Key Features:

• The present book is needed since there is a lack of literature with detailed elaboration and step-by-step calculations of different diffusion problems in terms of the Fox H-functions, Mittag-Leffler functions and other related special functions
• This book enables a clear introduction to students and researchers of the application of special functions in modern diffusion and random search problems