Fractional Dispersive Models and Applications

Fractional Dispersive Models and Applications
Title Fractional Dispersive Models and Applications PDF eBook
Author Panayotis G. Kevrekidis
Publisher Springer Nature
Pages 337
Release
Genre
ISBN 3031549783

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Advances in Fractional Calculus

Advances in Fractional Calculus
Title Advances in Fractional Calculus PDF eBook
Author J. Sabatier
Publisher Springer Science & Business Media
Pages 550
Release 2007-07-28
Genre Technology & Engineering
ISBN 1402060424

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In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models

Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models
Title Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models PDF eBook
Author Francesco Mainardi
Publisher World Scientific
Pages 368
Release 2010-05-18
Genre Mathematics
ISBN 1908978570

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This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types.It is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature given in the huge general bibliography.This book is likely to be of interest to applied scientists and engineers./a

Solving Frontier Problems of Physics: The Decomposition Method

Solving Frontier Problems of Physics: The Decomposition Method
Title Solving Frontier Problems of Physics: The Decomposition Method PDF eBook
Author G. Adomian
Publisher Springer Science & Business Media
Pages 367
Release 2013-06-29
Genre Science
ISBN 9401582890

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The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.

Transport & Fate of Chemicals in Soils

Transport & Fate of Chemicals in Soils
Title Transport & Fate of Chemicals in Soils PDF eBook
Author H. Magdi Selim
Publisher CRC Press
Pages 346
Release 2014-09-17
Genre Science
ISBN 1466557958

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During the last four decades, tremendous advances have been made towards the understanding of transport characteristics of contaminants in soils, solutes, and tracers in geological media. Transport & Fate of Chemicals in Soils: Principles & Applications offers a comprehensive treatment of the subject complete with supporting examples of mat

Fractals

Fractals
Title Fractals PDF eBook
Author Behzad Ghanbarian
Publisher CRC Press
Pages 289
Release 2017-11-23
Genre Mathematics
ISBN 1351648306

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This book provides theoretical concepts and applications of fractals and multifractals to a broad range of audiences from various scientific communities, such as petroleum, chemical, civil and environmental engineering, atmospheric research, and hydrology. In the first chapter, we introduce fractals and multifractals from physics and math viewpoints. We then discuss theory and practical applications in detail. In what follows, in chapter 2, fragmentation process is modeled using fractals. Fragmentation is the breaking of aggregates into smaller pieces or fragments, a typical phenomenon in nature. In chapter 3, the advantages and disadvantages of two- and three-phase fractal models are discussed in detail. These two kinds of approach have been widely applied in the literature to model different characteristics of natural phenomena. In chapter 4, two- and three-phase fractal techniques are used to develop capillary pressure curve models, which characterize pore-size distribution of porous media. Percolation theory provides a theoretical framework to model flow and transport in disordered networks and systems. Therefore, following chapter 4, in chapter 5 the fractal basis of percolation theory and its applications in surface and subsurface hydrology are discussed. In chapter 6, fracture networks are shown to be modeled using fractal approaches. Chapter 7 provides different applications of fractals and multifractals to petrophysics and relevant area in petroleum engineering. In chapter 8, we introduce the practical advantages of fractals and multifractals in geostatistics at large scales, which have broad applications in stochastic hydrology and hydrogeology. Multifractals have been also widely applied to model atmospheric characteristics, such as precipitation, temperature, and cloud shape. In chapter 9, these kinds of properties are addressed using multifractals. At watershed scales, river networks have been shown to follow fractal behavior. Therefore, the applications of fractals are addressed in chapter 10. Time series analysis has been under investigations for several decades in physics, hydrology, atmospheric research, civil engineering, and water resources. In chapter 11, we therefore, provide fractal, multifractal, multifractal detrended fluctuation analyses, which can be used to study temporal characterization of a phenomenon, such as flow discharge at a specific location of a river. Chapter 12 addresses signals and again time series using a novel fractal Fourier analysis. In chapter 13, we discuss constructal theory, which has a perspective opposite to fractal theories, and is based on optimizationof diffusive exchange. In the case of river drainages, for example, the constructal approach begins at the divide and generates headwater streams first, rather than starting from the fundamental drainage pattern.

Fractional Calculus and Fractional Differential Equations

Fractional Calculus and Fractional Differential Equations
Title Fractional Calculus and Fractional Differential Equations PDF eBook
Author Varsha Daftardar-Gejji
Publisher Springer
Pages 187
Release 2019-08-10
Genre Mathematics
ISBN 9811392277

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This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.