Theory and Applications of Fractional Differential Equations

Informationen zum Autor 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 di?erent parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scienti?c academies and scienti?c societies around the world, he is also actively associated editorially with numerous international scienti?c research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many Special Issues of scienti?c 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 Di?erence 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 scienti?c research journal articles, as well as Forewords and Prefaces to many books and journals. Klappentext This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. The subject of fractional calculus and its applications (that is! calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so! due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. Some of the areas of present-day applications of fractional models include Fluid Flow! Solute Transport or Dynamical Processes in Self-Similar and Porous Structures! Diffusive Transport akin to Diffusion! Material Viscoelastic Theory! Electromagnetic Theory! Dynamics of Earthquakes! Control Theory of Dynamical Systems! Optics and Signal Processing! Bio-Sciences! Economics! Geology! Astrophysics! Probability and Statistics! Chemical Physics! and so on. In the above-mentioned areas! there are phenomena with estrange kinetics which have a microscopic complex behaviour! and their macroscopic dynamics can not be characterized by classical derivative models. The fractional modelling is an emergent tool which use fractional differential equations including derivatives of fractional order! that is! we can spe...

Autorentext

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 di?erent parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scienti?c academies and scienti?c societies around the world, he is also actively associated editorially with numerous international scienti?c research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many Special Issues of scienti?c 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 Di?erence 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 scienti?c research journal articles, as well as Forewords and Prefaces to many books and journals.

Klappentext
This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus.
The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering.
Some of the areas of present-day applications of fractional models include Fluid Flow, Solute Transport or Dynamical Processes in Self-Similar and Porous Structures, Diffusive Transport akin to Diffusion, Material Viscoelastic Theory, Electromagnetic Theory, Dynamics of Earthquakes, Control Theory of Dynamical Systems, Optics and Signal Processing, Bio-Sciences, Economics, Geology, Astrophysics, Probability and Statistics, Chemical Physics, and so on.
In the above-mentioned areas, there are phenomena with estrange kinetics which have a microscopic complex behaviour, and their macroscopic dynamics can not be characterized by classical derivative models.
The fractional modelling is an emergent tool which use fractional differential equations including derivatives of fractional order, that is, we can speak about a derivative of order 1/3, or square root of 2, and so on. Some of such fractional models can have solutions which are non-differentiable but continuous functions, such as Weierstrass type functions. Su…