Local fractional integral transforms and their applications / Xiao Jun Yang, Dumitru Baleanu, H. M. Srivastava.

Format:

Book

Author/Creator:

Yang, Xiao Jun, author.

Baleanu, D. (Dumitru), author.

Srivastava, H. M., author.

Language:

English

Subjects (All):

Integral transforms.

Fractional integrals.

Physical Description:

1 online resource (484 p.)

Edition:

First edition.

Place of Publication:

Amsterdam, [Netherlands] : Elsevier, 2016.

Language Note:

English

Summary:

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 SeriesDiscusses definitions for local fractional Laplace transformsExplains local fractional Laplace transforms coupled with analytical methods

Contents:

Front Cover

Local Fractional Integral Transforms and Their Applications

Copyright

Contents

List of figures

List of tables

Preface

Chapter 1: Introduction to local fractional derivative and integral operators

1.1 Introduction

1.1.1 Definitions of local fractional derivatives

1.1.2 Comparisons of fractal relaxation equation in fractal kernel functions

1.1.3 Comparisons of fractal diffusion equation in fractal kernel functions

1.1.4 Fractional derivatives via fractional differences

1.1.5 Fractional derivatives with and without singular kernels and other versions of fractional derivatives

1.2 Definitions and properties of local fractional continuity

1.2.1 Definitions and properties

1.2.2 Functions defined on fractal sets

1.3 Definitions and properties of local fractional derivative

1.3.1 Definitions of local fractional derivative

1.3.2 Properties and theorems of local fractional derivatives

1.4 Definitions and properties of local fractional integral

1.4.1 Definitions of local fractional integrals

1.4.2 Properties and theorems of local fractional integrals

1.4.3 Local fractional Taylor's theorem for nondifferentiable functions

1.4.4 Local fractional Taylor's series for elementary functions

1.5 Local fractional partial differential equations in mathematical physics

1.5.1 Local fractional partial derivatives

1.5.2 Linear and nonlinear partial differential equations in mathematical physics

1.5.3 Applications of local fractional partial derivative operator to coordinate systems

1.5.4 Alternative observations of local fractional partial differential equations

Chapter 2: Local fractional Fourier series

2.1 Introduction

2.2 Definitions and properties

2.2.1 Analogous trigonometric form of local fractional Fourier series.

2.2.2 Complex Mittag-Leffler form of local fractional Fourier series

2.2.3 Properties of local fractional Fourier series

2.2.4 Theorems of local fractional Fourier series

2.3 Applications to signal analysis

2.4 Solving local fractional differential equations

2.4.1 Applications of local fractional ordinary differential equations

2.4.2 Applications of local fractional partial differential equations

Chapter 3: Local fractional Fourier transform and applications

3.1 Introduction

3.2 Definitions and properties

3.2.1 Mathematical mechanism is the local fractional Fourier transform operator

3.2.2 Definitions of the local fractional Fourier transform operators

3.2.3 Properties and theorems of local fractional Fourier transform operator

3.2.4 Properties and theorems of the generalized local fractional Fourier transform operator

3.3 Applications to signal analysis

3.3.1 The analogous distributions defined on Cantor sets

3.3.2 Applications of signal analysis on Cantor sets

3.4 Solving local fractional differential equations

3.4.1 Applications of local fractional ordinary differential equations

3.4.2 Applications of local fractional partial differential equations

Chapter 4: Local fractional Laplace transform and applications

4.1 Introduction

4.2 Definitions and properties

4.2.1 The basic definitions of the local fractional Laplace transform operators

4.2.2 The properties and theorems for the local fractional Laplace transform operator

4.3 Applications to signal analysis

4.4 Solving local fractional differential equations

4.4.1 Applications of local fractional ordinary differential equations

4.4.2 Applications of local fractional partial differential equations

Chapter 5: Coupling the local fractional Laplace transform with analytic methods

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

Back Cover.

Notes:

Description based upon print version of record

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed November 23, 2015).

ISBN:

9780128040324

0128040327

9780128040027

0128040025

OCLC:

929533584