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Book
Advanced Local Fractional Calculus and Its Applications
(2012)
  • Yang Xiaojun
Abstract

This book is the first international book to study theory and applications of local fractional calculus (LFC). It is an invitation both to the interested scientists and the engineers. It presents a thorough introduction to the recent results of local fractional calculus. It is also devoted to the application of advanced local fractional calculus on the mathematics science and engineering problems. The author focuses on multivariable local fractional calculus providing the general framework. It leads to new challenging insights and surprising correlations between fractal and fractional calculus. Keywords: Fractals - Mathematical complexity book - Local fractional calculus- Local fractional partial derivatives - Fractal Lagrange multipliers method - Multiple local fractional integrals - Local fractional gradient-Local fractional divergence theorem- Local fractional Stokes theorem- Green's first theorem in fractal domain- Green's second theorem in fractal domain - Fractal Riemann space - Geometry in fractal Riemann space - Fractal orthogonal coordinate tensors- Local fractional Euler–Lagrange equations - Principle of minimum potential energy in fractal medium- Principle of minimum potential energy in fractal medium - Principle of minimum complementary energy in fractal medium - J-integral formula in fractal fracture mechanics - Local fractional heat conduction equations Related subjects: Fractals- Complexity-Local Fractional Calculus And Applications- Fractal fracture mechanics- Fractal elasticity- Fractal heat conduction- Conservation of mass in fractal domain-Fractal transport equation- Fractal electromagnetic Table of contents  Preliminary Results  Local Fractional Calculus of One-variable Function  Local Fractional Partial Derivatives and Fractal Lagrange Multipliers Method  Multiple Local Fractional Integrals of Functions on Cantor Set  Local Fractional Line Integrals, Surface Integrals and Tensors  Local Fractional Calculus of Variations  A New Optimization Method for Functions on Cantor Set  Local Fractional Euler–Lagrange Equations  Applications of Local Fractional Calculus to Mechanics

Keywords
  • Fractals - Mathematical complexity book - Local fractional calculus- Local fractional partial derivatives - Fractal Lagrange multipliers method - Multiple local fractional integrals - Local fractional gradient-Local fractional divergence theorem- Local fractional Stokes theorem- Green's first theorem in fractal domain- Green's second theorem in fractal domain - Fractal Riemann space - Geometry in fractal Riemann space - Fractal orthogonal coordinate tensors- Local fractional Euler–Lagrange equations - Principle of minimum potential energy in fractal medium- Principle of minimum potential energy in fractal medium - Principle of minimum complementary energy in fractal medium - J-integral formula in fractal fracture mechanics - Local fractional heat conduction equations
Publication Date
2012
Editor
Xiao-Jun Yang
Publisher
World Science Publisher
ISBN
978-1-938576-01-0
Publisher Statement
This book is coprighted by Xiao-Jun Yang.
Citation Information
X. J. Yang, Advanced Local Fractional Calculus and Its Applications. New York: World Science Publisher, 2012.