Local Fractional Integral Transforms and Their Applications

Local Fractional Integral Transforms and Their Applications

1st Edition - October 1, 2015

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  • Authors: Xiao Jun Yang, Dumitru Baleanu, H. M. Srivastava
  • eBook ISBN: 9780128040324
  • Hardcover ISBN: 9780128040027

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Description

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.

Key Features

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

Readership

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

Table of Contents

    • 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

Product details

  • No. of pages: 262
  • Language: English
  • Copyright: © Academic Press 2015
  • Published: October 1, 2015
  • Imprint: Academic Press
  • eBook ISBN: 9780128040324
  • Hardcover ISBN: 9780128040027

About the Authors

Xiao Jun Yang

Xiao Jun Yang
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.

Affiliations and Expertise

Full Professor, China University of Mining and Technology, Xuzhou, China

Dumitru Baleanu

Dumitru Baleanu
Dumitru Baleanu is a professor at the Institute of Space Sciences, Magurele-Bucharest, Romania and a visiting staff member at the Department of Mathematics, Çankaya, University, Ankara, Turkey. He received his Ph.D. from the Institute of Atomic Physics in 1996. His fields of interest include Fractional Dynamics and its applications, Fractional Differential Equations and their applications, Discrete Mathematics, Image Processing, Bioinformatics, Mathematical Biology, Mathematical Physics, Soliton Theory, Lie Symmetry, Dynamic Systems on time scales, Computational Complexity, the Wavelet Method and its applications, Quantization of systems with constraints, the Hamilton-Jacobi Formalism, as well as geometries admitting generic and non-generic symmetries.

Affiliations and Expertise

Professor, Institute of Space Sciences, Magurele-Bucharest, Romania

H. M. Srivastava

Hari Mohan Srivastava works in the Department of Mathematics at University of Victoria, Victoria, British Columbia, BC, Canada

Affiliations and Expertise

Department of Mathematics, University of Victoria, Victoria, British Columbia, BC, Canada

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