Fractional Operators with Constant and Variable Order with Application to Geo hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author’s analyses, the book proposes new techniques for groundwater remediation, including guidelines on how chemical companies can be positioned in any city to avoid groundwater pollution. Proposes new aquifer derivatives for leaky, confined and unconfined formations Presents useful aids for applied scientists and engineers seeking to solve complex problems that cannot be handled using constant fractional order derivatives Provides a real physical interpretation of operators relevant to groundwater flow problems Models both fractional and variable order derivatives, presented together with uncertainties analysis

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  • Author : Abdon Atangana
  • Publisher : Academic Press
  • Pages : 414 pages
  • ISBN : 0128097965
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKFractional Operators with Constant and Variable Order with Application to Geo hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology
  • Author : Abdon Atangana
  • Publisher : Academic Press
  • Release : 19 September 2017
GET THIS BOOKFractional Operators with Constant and Variable Order with Application to Geo-hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author’s analyses, the book proposes new techniques for groundwater remediation,

Fractional Calculus for Hydrology, Soil Science and Geomechanics

Fractional Calculus for Hydrology, Soil Science and Geomechanics
  • Author : Ninghu Su
  • Publisher : CRC Press
  • Release : 02 November 2020
GET THIS BOOKFractional Calculus for Hydrology, Soil Science and Geomechanics

This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer. It is an integrated resource with theory and applications for

Numerical Methods for Fractional Differentiation

Numerical Methods for Fractional Differentiation
  • Author : Kolade M. Owolabi,Abdon Atangana
  • Publisher : Springer
  • Release : 24 October 2019
GET THIS BOOKNumerical Methods for Fractional Differentiation

This book discusses numerical methods for solving partial differential and integral equations, as well as ordinary differential and integral equations, involving fractional differential and integral operators. Differential and integral operators presented in the book include those with exponential decay law, known as Caputo–Fabrizio differential and integral operators, those with power law, known as Riemann–Liouville fractional operators, and those for the generalized Mittag–Leffler function, known as the Atangana–Baleanu fractional operators. The book reviews existing numerical schemes associated

Fractional Derivatives with Mittag-Leffler Kernel

Fractional Derivatives with Mittag-Leffler Kernel
  • Author : José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
  • Publisher : Springer
  • Release : 13 February 2019
GET THIS BOOKFractional Derivatives with Mittag-Leffler Kernel

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned

Mathematics Applied to Engineering, Modelling, and Social Issues

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  • Author : Frank T. Smith,Hemen Dutta,John N. Mordeson
  • Publisher : Springer
  • Release : 14 March 2019
GET THIS BOOKMathematics Applied to Engineering, Modelling, and Social Issues

This book presents several aspects of research on mathematics that have significant applications in engineering, modelling and social matters, discussing a number of current and future social issues and problems in which mathematical tools can be beneficial. Each chapter enhances our understanding of the research problems in a particular an area of study and highlights the latest advances made in that area. The self-contained contributions make the results and problems discussed accessible to readers, and provides references to enable those

Derivative with a New Parameter

Derivative with a New Parameter
  • Author : Abdon Atangana
  • Publisher : Academic Press
  • Release : 18 September 2015
GET THIS BOOKDerivative with a New Parameter

Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then

Advances in Numerical Methods

Advances in Numerical Methods
  • Author : Nikos Mastorakis,John Sakellaris
  • Publisher : Springer Science & Business Media
  • Release : 09 July 2009
GET THIS BOOKAdvances in Numerical Methods

Recent Advances in Numerical Methods features contributions from distinguished researchers, focused on significant aspects of current numerical methods and computational mathematics. The increasing necessity to present new computational methods that can solve complex scientific and engineering problems requires the preparation of this volume with actual new results and innovative methods that provide numerical solutions in effective computing times. Each chapter will present new and advanced methods and modern variations on known techniques that can solve difficult scientific problems efficiently.

Discrete Fractional Calculus

Discrete Fractional Calculus
  • Author : Christopher Goodrich,Allan C. Peterson
  • Publisher : Springer
  • Release : 09 February 2016
GET THIS BOOKDiscrete Fractional Calculus

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed

Handbook of Measure Theory

Handbook of Measure Theory
  • Author : E. Pap
  • Publisher : Elsevier
  • Release : 31 October 2002
GET THIS BOOKHandbook of Measure Theory

The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and

Water Resource Systems Planning and Management

Water Resource Systems Planning and Management
  • Author : Daniel P. Loucks,Eelco van Beek
  • Publisher : Springer
  • Release : 02 March 2017
GET THIS BOOKWater Resource Systems Planning and Management

This book is open access under a CC BY-NC 4.0 license. This revised, updated textbook presents a systems approach to the planning, management, and operation of water resources infrastructure in the environment. Previously published in 2005 by UNESCO and Deltares (Delft Hydraulics at the time), this new edition, written again with contributions from Jery R. Stedinger, Jozef P. M. Dijkman, and Monique T. Villars, is aimed equally at students and professionals. It introduces readers to the concept of viewing issues involving water

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

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  • Author : Elina Shishkina,Sergei Sitnik
  • Publisher : Academic Press
  • Release : 24 July 2020
GET THIS BOOKTransmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. Presents the universal

Fractional Differential Equations

Fractional Differential Equations
  • Author : Igor Podlubny
  • Publisher : Elsevier
  • Release : 27 October 1998
GET THIS BOOKFractional Differential Equations

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical

Water Quality Assessments

Water Quality Assessments
  • Author : Deborah V Chapman
  • Publisher : CRC Press
  • Release : 22 August 1996
GET THIS BOOKWater Quality Assessments

This guidebook, now thoroughly updated and revised in its second edition, gives comprehensive advice on the designing and setting up of monitoring programmes for the purpose of providing valid data for water quality assessments in all types of freshwater bodies. It is clearly and concisely written in order to provide the essential information for all agencies and individuals responsible for the water quality.

The Mathematics of the Uncertain

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  • Author : Eduardo Gil,Eva Gil,Juan Gil,María Ángeles Gil
  • Publisher : Springer
  • Release : 28 February 2018
GET THIS BOOKThe Mathematics of the Uncertain

This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and

Handbook of Mathematical Geosciences

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  • Author : B.S. Daya Sagar,Qiuming Cheng,Frits Agterberg
  • Publisher : Springer
  • Release : 25 June 2018
GET THIS BOOKHandbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory