Local Fractional Integral Transforms and Their Applications
- 1st Edition - October 12, 2015
- Authors: Xiao-Jun Yang, Dumitru Baleanu, Hari M Srivastava
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 8 0 4 0 0 2 - 7
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 0 4 0 3 2 - 4
Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widesp… Read more
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
- Edition: 1
- Published: October 12, 2015
- Language: English
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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, ChinaDB
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, RomaniaHS
Hari M Srivastava
Dr. Hari M. Srivastava is Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria, British Columbia, Canada. He earned his Ph.D. degree in 1965 while he was a full-time member of the teaching faculty at the Jai Narain Vyas University of Jodhpur, India. Dr. Srivastava has held (and continues to hold) numerous Visiting, Honorary and Chair Professorships at many universities and research institutes in different parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scientific academies and scientific societies around the world, he is also actively associated editorially with numerous international scientific research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many Special Issues of scientific research journals as the Lead or Joint Guest Editor, including the MDPI journal Axioms, Mathematics, and Symmetry, the Elsevier journals, Journal of Computational and Applied Mathematics, Applied Mathematics and Computation, Chaos, Solitons & Fractals, Alexandria Engineering Journal, and Journal of King Saud University – Science, the Wiley journal, Mathematical Methods in the Applied Sciences, the Springer journals, Advances in Difference Equations, Journal of Inequalities and Applications, Fixed Point Theory and Applications, and Boundary Value Problems, the American Institute of Physics journal, Chaos: An Interdisciplinary Journal of Nonlinear Science, and the American Institute of Mathematical Sciences journal, AIMS Mathematics, among many others. Dr. Srivastava has been a Clarivate Analytics (Web of Science) Highly-Cited Researcher since 2015. Dr. Srivastava’s research interests include several areas of Pure and Applied Mathematical Sciences, such as Real and Complex Analysis, Fractional Calculus and Its Applications, Integral Equations and Transforms, Higher Transcendental Functions and Their Applications, q-Series and q-Polynomials, Analytic Number Theory, Analytic and Geometric Inequalities, Probability and Statistics, and Inventory Modeling and Optimization. He has published 36 books, monographs, and edited volumes, 36 book (and encyclopedia) chapters, 48 papers in international conference proceedings, and more than 1450 peer-reviewed international scientific research journal articles, as well as Forewords and Prefaces to many books and journals.
Affiliations and expertise
Professor Emeritus, Department of Mathematics and Statistics, University of Victoria, British Columbia, CanadaRead Local Fractional Integral Transforms and Their Applications on ScienceDirect