Local Fractional Integral Transforms and Their Applications.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.