Local Fractional Integral Transforms and Their Applications

Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms.

• Provides applications of local fractional Fourier Series
• Discusses definitions for local fractional Laplace transforms
• Explains local fractional Laplace transforms coupled with analytical methods

Scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students

• List of figures
• List of tables
• Preface
• 1: Introduction to local fractional derivative and integral operators
  • Abstract
  • 1.1 Introduction
  • 1.2 Definitions and properties of local fractional continuity
  • 1.3 Definitions and properties of local fractional derivative
  • 1.4 Definitions and properties of local fractional integral
  • 1.5 Local fractional partial differential equations in mathematical physics
• 2: Local fractional Fourier series
  • Abstract
  • 2.1 Introduction
  • 2.2 Definitions and properties
  • 2.3 Applications to signal analysis
  • 2.4 Solving local fractional differential equations
• 3: Local fractional Fourier transform and applications
  • Abstract
  • 3.1 Introduction
  • 3.2 Definitions and properties
  • 3.3 Applications to signal analysis
  • 3.4 Solving local fractional differential equations
• 4: Local fractional Laplace transform and applications
  • Abstract
  • 4.1 Introduction
  • 4.2 Definitions and properties
  • 4.3 Applications to signal analysis
  • 4.4 Solving local fractional differential equations
• 5: Coupling the local fractional Laplace transform with analytic methods
  • Abstract
  • 5.1 Introduction
  • 5.2 Variational iteration method of the local fractional operator
  • 5.3 Decomposition method of the local fractional operator
  • 5.4 Coupling the Laplace transform with variational iteration method of the local fractional operator
  • 5.5 Coupling the Laplace transform with decomposition method of the local fractional operator
• Appendix A: The analogues of trigonometric functions defined on Cantor sets
• Appendix B: Local fractional derivatives of elementary functions
• Appendix C: Local fractional Maclaurin’s series of elementary functions
• Appendix D: Coordinate systems of Cantor-type cylindrical and Cantor-type spherical coordinates
• Appendix E: Tables of local fractional Fourier transform operators
• Appendix F: Tables of local fractional Laplace transform operators
• Bibliography
• Index