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

• Author : Abdon Atangana
• Release Date : 2017-09-19
• Genre: Mathematics
• Pages : 414
• ISBN 10 : 9780128097960

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

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

## Fractional Operators with Constant and Variable Order with Application to Geo Hydrology

• Author : Abdon Atangana
• Release Date : 2017-09-22
• Genre: Uncategoriezed
• Pages : 414
• ISBN 10 : 0128096705

Fractional Operators with Constant and Variable Order with Application to Geo Hydrology Excerpt :

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

## Fractional Calculus for Hydrology Soil Science and Geomechanics

• Author : Ninghu Su
• Publisher : CRC Press
• Release Date : 2020-11-02
• Genre: Science
• Pages : 410
• ISBN 10 : 9781351032407

Fractional Calculus for Hydrology Soil Science and Geomechanics Excerpt :

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 those interested in hydrology, hydraulics and fluid mechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications.

## Fractional Derivatives with Mittag Leffler Kernel

• Author : José Francisco Gómez
• Publisher : Springer
• Release Date : 2019-02-13
• Genre: Technology & Engineering
• Pages : 341
• ISBN 10 : 9783030116620

Fractional Derivatives with Mittag Leffler Kernel Excerpt :

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 areas.

## Fractional Order Analysis

• Author : Hemen Dutta
• Publisher : John Wiley & Sons
• Release Date : 2020-08-06
• Genre: Mathematics
• Pages : 336
• ISBN 10 : 9781119654230

Fractional Order Analysis Excerpt :

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 range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.

## Methods of Mathematical Modelling

• Author : Harendra Singh
• Publisher : CRC Press
• Release Date : 2019-09-17
• Genre: Technology & Engineering
• Pages : 168
• ISBN 10 : 9781000606485

Methods of Mathematical Modelling Excerpt :

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 interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications

## Mathematics Applied to Engineering Modelling and Social Issues

• Author : Frank T. Smith
• Publisher : Springer
• Release Date : 2019-03-14
• Genre: Technology & Engineering
• Pages : 699
• ISBN 10 : 9783030122324

Mathematics Applied to Engineering Modelling and Social Issues Excerpt :

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 interested to follow subsequent studies in still developing fields. Presenting real-world applications, the book is a valuable resource for graduate students, researchers and educators. It appeals to general readers curious about the practical applications of mathematics in diverse scientific areas and social problems.

## Basic Theory

• Author : Anatoly Kochubei
• Publisher : Walter de Gruyter GmbH & Co KG
• Release Date : 2019-02-19
• Genre: Mathematics
• Pages : 489
• ISBN 10 : 9783110571622

Basic Theory Excerpt :

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.

## Numerical Methods for Fractional Differentiation

• Author : Kolade M. Owolabi
• Publisher : Springer Nature
• Release Date : 2019-10-14
• Genre: Mathematics
• Pages : 328
• ISBN 10 : 9789811500985

Numerical Methods for Fractional Differentiation Excerpt :

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 with fractional operators including those with power law, while also highlighting new trends in numerical schemes for recently introduced differential and integral operators. In addition, the initial chapters address useful properties of each differential and integral fractional operator. Methods discussed in the book are subsequently used to solved problems arising in many fields of science, technology, and engineering, including epidemiology, chaos, solitons, fractals, diffusion, groundwater, and fluid mechanics. Given its scope, the book offers a valuable resource for graduate students of mathematics and engineering, and researchers in virtually all fields of science, technology, and engineering, as well as an excellent addition to libraries.

## 13th Chaotic Modeling and Simulation International Conference

• Author : Christos H. Skiadas
• Publisher : Springer Nature
• Release Date : 2021
• Genre: Chaotic behavior in systems
• Pages : 1080
• ISBN 10 : 9783030707958

13th Chaotic Modeling and Simulation International Conference Excerpt :

Gathering the proceedings of the 13th CHAOS2020 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.

## Communication and Intelligent Systems

• Author : Harish Sharma
• Publisher : Springer Nature
• Release Date : 2021-06-28
• Genre: Technology & Engineering
• Pages : 1040
• ISBN 10 : 9789811610899

Communication and Intelligent Systems Excerpt :

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 smart communication technologies. The book presents single- and multi-disciplinary research on these themes in order to make the latest results available in a single, readily accessible source.

## Porous Fluids

• Author : Vallampati Ramachandra Prasad
• Publisher : BoD – Books on Demand
• Release Date : 2021-08-18
• Genre: Science
• Pages : 134
• ISBN 10 : 9781839627118

Porous Fluids Excerpt :

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.

Score: 4.5
From 3 Ratings

## Fractional Differential Equations

• Author : Igor Podlubny
• Publisher : Elsevier
• Release Date : 1998-10-27
• Genre: Mathematics
• Pages : 340
• ISBN 10 : 0080531989

Fractional Differential Equations Excerpt :

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 models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

## Mathematical Economics

• Author : Vasily E. Tarasov
• Publisher : MDPI
• Release Date : 2020-06-03
• Pages : 278
• ISBN 10 : 9783039361182

Mathematical Economics Excerpt :

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

## Fractional Differential Equations

• Author : Anatoly Kochubei
• Publisher : Walter de Gruyter GmbH & Co KG
• Release Date : 2019-02-19
• Genre: Mathematics
• Pages : 527
• ISBN 10 : 9783110571660

Fractional Differential Equations Excerpt :

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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.