June 2024
Intermediate to advanced
250 pages
9h 12m
English
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1: Introduction to fractional calculus
Abstract
This chapter aims to provide an introduction to fractional calculus, a tool that generalizes classical calculus. It explores the history and development of fractional calculus, discussing the differences between classical and fractional calculus, as well as local and non-local fractional operators. The chapter also covers some prerequisite special functions, such as the gamma function, beta function, complementary error function, Mittag-Leffler function, Laplace transformation, and convolution. It then delves into various types of fractional derivatives, including Riemann–Liouville fractional differentiation, Caputo fractional derivative, Grünwald–Letnikov derivative, Caputo–Fabrizio fractional differentiation, ...
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