Fractional Operators With Constant And Variable Order With Application To Geo Hydrology

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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 Date : 2017-09-22
  • Total pages : 414
  • ISBN : 0128096705
  • File Size : 45,9 Mb
  • Total Download : 470
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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

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology
  • Author : Abdon Atangana
  • Publisher : Academic Press
  • Release Date : 2017-09-19
  • Total pages : 414
  • ISBN : 9780128097960
  • File Size : 37,9 Mb
  • Total Download : 307
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Download Fractional Operators with Constant and Variable Order with Application to Geo-hydrology in PDF, Epub, and Kindle

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

Fractional Calculus for Hydrology, Soil Science and Geomechanics
  • Author : Ninghu Su
  • Publisher : CRC Press
  • Release Date : 2020-11-02
  • Total pages : 410
  • ISBN : 9781351032407
  • File Size : 46,6 Mb
  • Total Download : 573
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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

Fractional Derivatives with Mittag-Leffler Kernel
  • Author : José Francisco Gómez,Lizeth Torres,Ricardo Fabricio Escobar
  • Publisher : Springer
  • Release Date : 2019-02-13
  • Total pages : 341
  • ISBN : 9783030116620
  • File Size : 45,7 Mb
  • Total Download : 166
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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

Fractional Order Analysis
  • Author : Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana
  • Publisher : John Wiley & Sons
  • Release Date : 2020-08-06
  • Total pages : 336
  • ISBN : 9781119654230
  • File Size : 36,5 Mb
  • Total Download : 657
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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

Methods of Mathematical Modelling
  • Author : Harendra Singh,Devendra Kumar,Dumitru Baleanu
  • Publisher : CRC Press
  • Release Date : 2019-09-17
  • Total pages : 168
  • ISBN : 9781000606485
  • File Size : 16,9 Mb
  • Total Download : 238
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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

Mathematics Applied to Engineering, Modelling, and Social Issues
  • Author : Frank T. Smith,Hemen Dutta,John N. Mordeson
  • Publisher : Springer
  • Release Date : 2019-03-14
  • Total pages : 699
  • ISBN : 9783030122324
  • File Size : 42,9 Mb
  • Total Download : 678
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Download Mathematics Applied to Engineering, Modelling, and Social Issues in PDF, Epub, and Kindle

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.

Untitled

Untitled
  • Author : Anonim
  • Publisher : Springer Nature
  • Release Date : 2023
  • Total pages : 510
  • ISBN : 9789464630145
  • File Size : 36,5 Mb
  • Total Download : 104
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Download Untitled in PDF, Epub, and Kindle

PDF book entitled Untitled written by Anonim and published by Springer Nature which was released on 2023 with total hardcover pages 510, the book become popular and critical acclaim.

Basic Theory

Basic Theory
  • Author : Anatoly Kochubei,Yuri Luchko
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2019-02-19
  • Total pages : 489
  • ISBN : 9783110571622
  • File Size : 26,8 Mb
  • Total Download : 705
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Download Basic Theory in PDF, Epub, and Kindle

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

Numerical Methods for Fractional Differentiation
  • Author : Kolade M. Owolabi,Abdon Atangana
  • Publisher : Springer Nature
  • Release Date : 2019-10-14
  • Total pages : 328
  • ISBN : 9789811500985
  • File Size : 54,6 Mb
  • Total Download : 463
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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

13th Chaotic Modeling and Simulation International Conference
  • Author : Christos H. Skiadas,Yiannis Dimotikalis
  • Publisher : Springer Nature
  • Release Date : 2021-12-14
  • Total pages : 1080
  • ISBN : 9783030707958
  • File Size : 13,5 Mb
  • Total Download : 329
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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

Communication and Intelligent Systems
  • Author : Harish Sharma,Mukesh Kumar Gupta,G. S. Tomar,Wang Lipo
  • Publisher : Springer Nature
  • Release Date : 2021-06-28
  • Total pages : 1040
  • ISBN : 9789811610899
  • File Size : 36,6 Mb
  • Total Download : 198
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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

Porous Fluids
  • Author : Vallampati Ramachandra Prasad
  • Publisher : BoD – Books on Demand
  • Release Date : 2021-08-18
  • Total pages : 134
  • ISBN : 9781839627118
  • File Size : 54,9 Mb
  • Total Download : 485
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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.

Fractional Differential Equations

Fractional Differential Equations
  • Author : Igor Podlubny
  • Publisher : Elsevier
  • Release Date : 1998-10-27
  • Total pages : 340
  • ISBN : 0080531989
  • File Size : 51,9 Mb
  • Total Download : 749
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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

Nature’s Patterns and the Fractional Calculus

Nature’s Patterns and the Fractional Calculus
  • Author : Bruce J. West
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2017-09-11
  • Total pages : 213
  • ISBN : 9783110535136
  • File Size : 21,5 Mb
  • Total Download : 916
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Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus

Water Resource Systems Planning and Management

Water Resource Systems Planning and Management
  • Author : Daniel P. Loucks,Eelco van Beek
  • Publisher : Springer
  • Release Date : 2017-03-02
  • Total pages : 624
  • ISBN : 9783319442341
  • File Size : 15,9 Mb
  • Total Download : 152
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Download Water Resource Systems Planning and Management in PDF, Epub, and Kindle

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 resources as a system of multiple interacting components and scales. It offers guidelines for initiating and carrying out water resource system planning and management projects. It introduces alternative optimization, simulation, and statistical methods useful for project identification, design, siting, operation and evaluation and for studying post-planning issues. The authors cover both basin-wide and urban water issues and present ways of identifying and evaluating alternatives for addressing multiple-purpose and multi-objective water quantity and quality management challenges. Reinforced with cases studies, exercises, and media supplements throughout, the text is ideal for upper-level undergraduate and graduate courses in water resource planning and management as well as for practicing planners and engineers in the field.

Numerical Methods for Fractional Differentiation

Numerical Methods for Fractional Differentiation
  • Author : Kolade M. Owolabi,Abdon Atangana
  • Publisher : Springer
  • Release Date : 2019-10-24
  • Total pages : 328
  • ISBN : 9811500975
  • File Size : 23,9 Mb
  • Total Download : 237
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Download Numerical Methods for Fractional Differentiation in PDF, Epub, and Kindle

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.

The Variable-Order Fractional Calculus of Variations

The Variable-Order Fractional Calculus of Variations
  • Author : Ricardo Almeida,Dina Tavares,Delfim F. M. Torres
  • Publisher : Springer
  • Release Date : 2018-06-29
  • Total pages : 124
  • ISBN : 9783319940069
  • File Size : 24,9 Mb
  • Total Download : 814
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​The Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one, an approximation formula is obtained in terms of standard (integer-order) derivatives only. Estimations for the error of the approximations are also provided. The contributors consider variational problems that may be subject to one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. In particular, they establish necessary optimality conditions of Euler–Lagrange type. As the terminal point in the cost integral is free, as is the terminal state, transversality conditions are also obtained. The Variable-Order Fractional Calculus of Variations is a valuable source of information for researchers in mathematics, physics, engineering, control and optimization; it provides both analytical and numerical methods to deal with variational problems. It is also of interest to academics and postgraduates in these fields, as it solves multiple variational problems subject to one or more constraints in a single brief.

New Numerical Scheme with Newton Polynomial

New Numerical Scheme with Newton Polynomial
  • Author : Abdon Atangana,Seda Igret Araz
  • Publisher : Academic Press
  • Release Date : 2021-06-10
  • Total pages : 460
  • ISBN : 9780323858021
  • File Size : 42,8 Mb
  • Total Download : 353
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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 new schemes for fractional calculus. Final sections include six chapters on the application of numerical scheme to a range of real-world applications. Over the last several decades, many techniques have been suggested to model real-world problems across science, technology and engineering. New analytical methods have been suggested in order to provide exact solutions to real-world problems. Many real-world problems, however, cannot be solved using analytical methods. To handle these problems, researchers need to rely on numerical methods, hence the release of this important resource on the topic at hand. Offers an overview of the field of numerical analysis and modeling real-world problems Provides a deeper understanding and comparison of Adams-Bashforth and Newton polynomial numerical methods Presents applications of local fractional calculus to a range of real-world problems Explores new scheme for fractal functions and investigates numerical scheme for partial differential equations with integer and non-integer order Includes codes and examples in MATLAB in all relevant chapters

Computational Methods for Multiphase Flows in Porous Media

Computational Methods for Multiphase Flows in Porous Media
  • Author : Zhangxin Chen,Guanren Huan,Yuanle Ma
  • Publisher : SIAM
  • Release Date : 2006-04-01
  • Total pages : 551
  • ISBN : 9780898716061
  • File Size : 40,8 Mb
  • Total Download : 675
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This book offers a fundamental and practical introduction to the use of computational methods. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises.

General Fractional Derivatives

General Fractional Derivatives
  • Author : Xiao-Jun Yang
  • Publisher : CRC Press
  • Release Date : 2019-05-10
  • Total pages : 364
  • ISBN : 9780429811531
  • File Size : 48,7 Mb
  • Total Download : 481
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General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.