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Fractal Vector Analysis

  • Book
  • 300 Pages
  • September 2021
  • Elsevier Science and Technology
  • ID: 5308633

Fractal Vector Analysis: A Local Fractional Calculus Point of View provides an overview of fractal vector calculus, which includes local fractional line integrals, local fractional surface integrals, and local fractional volume integrals. The book presents an overview of key breakthroughs in classical calculus in vector spaces. Readers will gain a deeper understanding of some applications of local fractional calculus from the fractals point of view. Coverage will include double and triple local fractional integrals, as well as elliptic, parabolic and hyperbolic local fractional PDEs.

The potential audience includes, but is not limited to, researchers in the fields of mathematics, physics, and engineering. It could also be used as a textbook for an introductory course on fractal vector calculus and applications, for senior undergraduate and graduate students in the above-mentioned areas.

  • Provides a deeper understanding of many applications of local fractional calculus from the fractals point of view
  • Presents a historical overview of local fractional calculus and explores a range of potential applications for real-world problems in science and engineering
  • Explores a novel optimization method for fractal functions and investigates local fractional Fourier type integral transform

Table of Contents

1. Preliminaries 2. Local fractional calculus of one-variable functions defined on fractal sets 3. Local fractional partial derivatives and applications 4. Multiple local fractional integrals of fractal functions 5. Local fractional line integrals, surface integrals and tensors 6. Local fractional calculus of variations 7. A optimization method for fractal functions 8. Local fractional Euler-Lagrange type equations 9. Local fractional Fourier type integral transform 10. Applications


Yang, Xiao-Jun Dr. Xiao-Jun Yang is a full professor of China University of Mining and Technology, China. He was awarded the 2019 Obada-Prize, the Young Scientist Prize (Turkey), and Springer's Distinguished Researcher Award. His scientific interests include: Viscoelasticity, Mathematical Physics, Fractional Calculus and Applications, Fractals, Analytic Number Theory, and Special Functions. He has published over 160 journal articles and 4 monographs, 1 edited volume, and 10 chapters. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Methods in the Applied Sciences, Mathematical Modelling and Analysis, Journal of Thermal Stresses, and Thermal Science, and an associate editor of Journal of Thermal Analysis and Calorimetry, Alexandria Engineering Journal, and IEEE Access.