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Recent Trends in Fractional Calculus and Its Applications
Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.The term Fractional Calculus is more than 300 years old. It is a ge...
Urban Scaling
Urban allometry empirically describes how “things”, for example crime, GDP, emissions, energy use, area, street length, housing prices, etc. change in cities when their size, in terms of population, increases. Urban scaling is a relatively recent area of urban science, investigating how measurable characteristics of cities vary with their sizes. This book addresses this relatively novel but highly debated topic within urban studies and geography. It presents many results, techniques, methods, and reflections on urban scaling and allometry. The sections are organized into different sub- areas such as socio- economic, infrastructural or environmental outputs, so that there is a broad organ...
Numerical Methods for Fractal-Fractional Differential Equations and Engineering
This book is about the simulation and modeling of novel chaotic systems within the frame of fractal-fractional operators. The methods used, their convergence, stability, and error analysis are given, and this is the first book to offer mathematical modeling and simulations of chaotic problems with a wide range of fractal-fractional operators, to find solutions. Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling provides details for stability, convergence, and analysis along with numerical methods and their solution procedures for fractal-fractional operators. The book offers applications to chaotic problems and simulations using multiple fractal-fractional operators and concentrates on models that display chaos. The book details how these systems can be predictable for a while and then can appear to become random. Practitioners, engineers, researchers, and senior undergraduate and graduate students from mathematics and engineering disciplines will find this book of interest._
Mathematical Methods in Medical and Biological Sciences
Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits. In addition, the book provides leading-edge developments and insights for a range of applications, including epidemi...
Fractional Diffusion Equations and Anomalous Diffusion
Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.
Special Functions in Fractional Calculus and Engineering
Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the no...
Introduction to Urban Science
A novel, integrative approach to cities as complex adaptive systems, applicable to issues ranging from innovation to economic prosperity to settlement patterns. Human beings around the world increasingly live in urban environments. In Introduction to Urban Science, Luis Bettencourt takes a novel, integrative approach to understanding cities as complex adaptive systems, claiming that they require us to frame the field of urban science in a way that goes beyond existing theory in such traditional disciplines as sociology, geography, and economics. He explores the processes facilitated by and, in many cases, unleashed for the first time by urban life through the lenses of social heterogeneity, ...
Income Distribution Dynamics of Economic Systems
An overview of the distributive dynamics of economic systems in a broad theoretical and empirical sense from the econophysical viewpoint.
The Craft of Fractional Modelling in Science and Engineering
This book is a printed edition of the Special Issue "The Craft of Fractional Modelling in Science and Engineering" that was published in Fractal Fract
Statistics and Dynamics of Urban Populations
Urbanization is a fundamental process in human history and is increasingly affecting our environment and society. Although cities have existed for centuries, describing and controlling urbanization has always been difficult and still is: cities are continuously changing over time in a non-homogeneous fashion that has puzzled historians, geographers, philosophers, economists, urbanists, engineers, mathematicians and physicists. In particular, one of the most debated issues of urban studies has been the question of urban population growth. How do cities appear and disappear, grow or decline? Why do we observe a hierarchy of cities from small to large and not a typical city size ? These questio...
