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Essentials of Fractional Calculus

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Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 219))

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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.

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  1. Institute of Mathematics and Computer Science, Jan Długosz University, Częstochowa, Poland

    Yuriy Povstenko

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  1. Yuriy Povstenko
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Povstenko, Y. (2015). Essentials of Fractional Calculus. In: Fractional Thermoelasticity. Solid Mechanics and Its Applications, vol 219. Springer, Cham. https://doi.org/10.1007/978-3-319-15335-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-15335-3_1

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