Ascione G. Fractional Deterministic and Stochastic Calculus 2023

Textbook in PDF format

Fractional calculus has emerged as a powerful and effective mathematical tool in the study of several phenomena in science and engineering. This text addressed to researchers, graduate students, and practitioners combines deterministic fractional calculus with the analysis of the fractional Brownian motion and its associated fractional stochastic calculus and includes examples, exercises, and problems that focus on computational aspects.This text provides an overview of the elements of fractional analysis and processes, and includes a wide variety of hands-on applications and exercises that help the reader master the technique of calculations associated with fractional operators.
Introduction
Fractional integrals and derivatives
Integral and differential equations involving fractional operators
Fractional Brownian motion and its environment
Stochastic processes and fractional differential equations
Numerical methods and simulation