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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.
Preface
Acknowledgments
Acronyms and Symbols
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
Appendix A: Functional calculus
Appendix B: Stochastic differential equations
Appendix C: Large deviation principle
Appendix D: Fractals and fractal dimension
Appendix E: Implementation of Wolfram Mathematica
Index