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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
- 1: Introduction to local fractional derivative and integral operators
- 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
- 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
- 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
- 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
- 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
- No. of pages:
- © Academic Press 2015
- 1st October 2015
- Academic Press
- eBook ISBN:
- Hardcover ISBN:
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.
China University of Mining and Technology, Xuzhou, China
Dr. Dumitru Baleanu is a professor at the Institute of Space Sciences, Magurele-Bucharest, Romania and a visiting staff member at the Department of Mathematics, Cankaya University, Ankara, Turkey. Dr. Baleanu received his Phd 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. Dr. Baleanu is co-author of 15 books published by pringer, Elsevier and World Scientific. He has published more than 1000 ISI papers. Dumitru Baleanu won the 2019 Obada Prize. This prize recognizes and encourages innovative and interdisciplinary research that cuts across traditional boundaries and paradigms. It aims to foster universal values of excellence, creativity, justice, democracy, and progress and to promote the scientific, technological and humanistic achievements that advance and improve our world.
Professor, Institute of Space Sciences, Magurele-Bucharest, Romania
University of Victoria, Victoria, British Columbia, Canada University of Victoria, BC, Canada
"...a boon to all those who are interested in the eld of local fractional integral transforms and want to further develop this live and useful branch of mathematics." --Zentralblatt MATH
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