Numerical Methods for Fractional Differentiation

by Owolabi, Kolade M.

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Title Statements

Full title :Numerical Methods for Fractional Differentiation / Kolade M. Owoladi, Abdon Atangana.

Summary

This book discusses numerical methods for solving partial differential and integral equations, as well as ordinary differential and integral equations, involving fractional differential and integral operators. Differential and integral operators presented in the book include those with exponential decay law, known as Caputo-Fabrizio differential and integral operators, those with power law, known as Riemann-Liouville fractional operators, and those for the generalized Mittag-Leffler function, known as the Atangana-Baleanu fractional operators. The book reviews existing numerical schemes associated with fractional operators including those with power law, while also highlighting new trends in numerical schemes for recently introduced differential and integral operators. In addition, the initial chapters address useful properties of each differential and integral fractional operator. Methods discussed in the book are subsequently used to solved problems arising in many fields of science, technology, and engineering, including epidemiology, chaos, solitons, fractals, diffusion, groundwater, and fluid mechanics. Given its scope, the book offers a valuable resource for graduate students of mathematics and engineering, and researchers in virtually all fields of science, technology, and engineering, as well as an excellent addition to libraries.

Edition Statements

Publication Date:2019.

Publication Statements

Publisher(s):Springer
Place of Publication:Singapore
Language:eng
Publication Date:2019.

Notes

4.3.2 The New Fractional Adams-Bashforth Scheme with Caputo Derivative

The Physical Object

Description:1 online resource (338 pages)

Edition Identifiers

ISBN:9789811500985, 9811500983
oclc:on1124603463
LC Classification:QA314
Dewey Decimal:515/.35

Intro; Preface; Acknowledgements; Contents; About the Authors; 1 Review of Fractional Differentiation; 1.1 Special Functions; 1.1.1 The Gamma Function; 1.1.2 The Beta Function; 1.1.3 The Complementary Error Function; 1.1.4 The Mittag-Leffler Function; 1.1.5 Laplace Transformation and Convolution; 1.2 Riemann-Liouville Fractional Differentiation; 1.3 Caputo Fractional Derivative; 1.4 Classical Fractional Derivatives; 1.5 Partial Riemann-Liouville Fractional Derivative; 1.6 Fractional Operators with Variable Order; 1.7 Tempered Fractional Differentiation

1.7.1 Properties of Tempered Fractional Derivative and Integral1.7.2 Laplace Transforms of the Tempered Fractional Calculus; 1.8 Caputo-Fabrizio Fractional Differentiation; 1.8.1 Caputo-Fabrizio Fractional Derivative in Caputo Sense; 1.8.2 The Laplace Transform of the Caputo-Fabrizio Fractional Derivative; 1.8.3 Fourier Transform of Fractional Gradient, Divergence and Laplacian; 1.8.4 Caputo-Fabrizio Fractional Derivative in Riemann-Liouville Sense; 1.9 Stretch Fractional Differentiation; 1.10 The Atangana-Baleanu Fractional Derivative and Integral

1.11 The Riesz Potential and Riesz Fractional Derivatives1.11.1 The Atangana-Gómez …