# Essentials of Fractional Calculus

• Yuriy Povstenko
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 219)

## Abstract

Essentials of fractional calculus are presented. Different kinds of integral and differential operators of fractional order are discussed. The notion of the Riemann-Liouville fractional integral is introduced as a natural generalization of the repeated integral written in a convolution type form. The Riemann-Liouville fractional derivative is defined as left-inverse to the Riemann-Liouville fractional integral. The Caputo fractional derivative and the Riesz fractional operators (including the fractional Laplace operator) are considered. The cumbersome aspects of space-fractional differential operators disappear when one computes their Fourier integral transforms.

## Keywords

Fractional Order Fractional Derivative Fractional Calculus Fractional Differential Equation Fractional Integral
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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