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 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

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

Mathematics Applied to Engineering, Modelling, and Social Issues

Mathematics Applied to Engineering, Modelling, and Social Issues
  • 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

Methods of Mathematical Modelling

Methods of Mathematical Modelling
  • Author : Harendra Singh,Devendra Kumar,Dumitru Baleanu
  • Publisher : CRC Press
  • Release : 16 September 2019
GET THIS BOOKMethods of Mathematical Modelling

This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists

Fractional Order Analysis

Fractional Order Analysis
  • Author : Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana
  • Publisher : John Wiley & Sons
  • Release : 06 August 2020
GET THIS BOOKFractional Order Analysis

A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a

Numerical Methods for Fractional Differentiation

Numerical Methods for Fractional Differentiation
  • Author : Kolade M. Owolabi,Abdon Atangana
  • Publisher : Springer Nature
  • Release : 14 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

Communication and Intelligent Systems

Communication and Intelligent Systems
  • Author : Harish Sharma,Mukesh Kumar Gupta,Geetam Tomar,Wang Lipo
  • Publisher : Springer Nature
  • Release : 28 October 2021
GET THIS BOOKCommunication and Intelligent Systems

This book gathers selected research papers presented at the International Conference on Communication and Intelligent Systems (ICCIS 2020), organized jointly by Birla Institute of Applied Sciences, Uttarakhand, and Soft Computing Research Society during 26-27 December 2020. This book presents a collection of state-of-the-art research work involving cutting-edge technologies for communication and intelligent systems. Over the past few years, advances in artificial intelligence and machine learning have sparked new research efforts around the globe, which explore novel ways of developing intelligent systems and

Basic Theory

Basic Theory
  • Author : Anatoly Kochubei,Yuri Luchko
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 19 February 2019
GET THIS BOOKBasic Theory

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Porous Fluids

Porous Fluids
  • Author : Vallampati Ramachandra Prasad
  • Publisher : BoD – Books on Demand
  • Release : 18 August 2021
GET THIS BOOKPorous Fluids

Written by authoritative experts in the field, this book discusses fluid flow and transport phenomena in porous media. Portions of the book are devoted to interpretations of experimental results in this area and directions for future research. It is a useful reference for applied mathematicians and engineers, especially those working in the area of porous media.

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

New Numerical Scheme with Newton Polynomial

New Numerical Scheme with Newton Polynomial
  • Author : Abdon Atangana,Seda Igret Araz
  • Publisher : Academic Press
  • Release : 10 June 2021
GET THIS BOOKNew Numerical Scheme with Newton Polynomial

New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications provides a detailed discussion on the underpinnings of the theory, methods and real-world applications of this numerical scheme. The book's authors explore how this efficient and accurate numerical scheme is useful for solving partial and ordinary differential equations, as well as systems of ordinary and partial differential equations with different types of integral operators. Content coverage includes the foundational layers of polynomial interpretation, Lagrange interpolation, and Newton interpolation, followed by

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

Numerical Methods for Fractional Differentiation

Numerical Methods for Fractional Differentiation
  • Author : Kolade M. Owolabi,Abdon Atangana
  • Publisher : Springer
  • Release : 07 November 2020
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