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 BackgroundFox H-Function and Related FunctionsElements of Random Walk TheoryCTRW on CombsHeterogeneous Diffusion ProcessesDiffusion Processes with Stochastic ResettingRandom SearchDiffusion on Fractal TartanFinite-Velocity DiffusionAppendices: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 functionsThis book enables a clear introduction to students and researchers of the application of special functions in modern diffusion and random search problems