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Hausdorff Calculus: Applications to Fractal Systems

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This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.

Author(s): Yingjie Liang, Wen Chen, Wei Cai
Series: Fractional Calculus in Applied Sciences and Engineering 6
Publisher: De Gruyter
Year: 2019

Language: English
Pages: 150

Cover......Page 1
Hausdorff Calculus: Applications to Fractal Systems
......Page 5
© 2019......Page 6
Preface......Page 7
Contents
......Page 9
1 Introduction......Page 11
2 Hausdorff diffusion equation......Page 15
3 Statistics on fractals......Page 21
4 Lyapunov stability of Hausdorff derivative
non-linear systems......Page 37
5 Hausdorff radial basis function......Page 49
6 Hausdorff PDE modeling......Page 69
7 Local structural derivative......Page 119
8 Perspectives......Page 135
Bibliography
......Page 137
Index......Page 147