Fractional Operators with Constant and Variable Order with Application to Geo-hydrology PDF Download
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Author: Abdon Atangana
Publisher: Academic Press
ISBN: 0128097965
Category : Mathematics
Languages : en
Pages : 416
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Book Description
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
Author: Abdon Atangana
Publisher: Academic Press
ISBN: 0128097965
Category : Mathematics
Languages : en
Pages : 416
Get Book Here
Book Description
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
Author: Ninghu Su
Publisher: CRC Press
ISBN: 1351032402
Category : Science
Languages : en
Pages : 410
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Book Description
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.
Author: José Francisco Gómez
Publisher: Springer
ISBN: 303011662X
Category : Technology & Engineering
Languages : en
Pages : 339
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Book Description
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.
Author: Hemen Dutta
Publisher: John Wiley & Sons
ISBN: 1119654238
Category : Mathematics
Languages : en
Pages : 336
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Book Description
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.
Author: Harendra Singh
Publisher: CRC Press
ISBN: 1000606481
Category : Technology & Engineering
Languages : en
Pages : 231
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Book Description
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
Author: Anatoly Kochubei
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110570637
Category : Mathematics
Languages : en
Pages : 683
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Book Description
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.
Author: Frank T. Smith
Publisher: Springer
ISBN: 3030122328
Category : Technology & Engineering
Languages : en
Pages : 703
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Book Description
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.
Author: Nadihah Wahi
Publisher: Springer Nature
ISBN: 9464630140
Category : Mathematics
Languages : en
Pages : 510
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Book Description
This is an open access book. The ICMSS2022 is an international conference jointly organised by the Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia together with the Banasthali University, Jaipur, India. This international conference aims to give exposure and to bring together academicians, researchers and industry experts for intellectual growth. The ICMSS2022 serves as a platform for the scientific community members to exchange ideas and approaches, to present research findings, and to discuss current issues and topics related to mathematics, statistics as well as their applications. Objectives: to present the most recent discoveries in mathematics and statistics. to serve as a platform for knowledge and information sharing between experts from industries and academia. to identify and create potential collaboration among participants. The organising committee of ICMSS2022 welcomes all delegates to deliberate over various aspects related to the conference themes and sub-themes.
Author: Saïd Abbas
Publisher: Elsevier
ISBN: 044323602X
Category : Computers
Languages : en
Pages : 400
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Book Description
The field of fractional calculus (FC) is more than 300 years old, and it presumably stemmed from a question about a fractional-order derivative raised in communication between L'Hopital and Leibniz in the year 1695. This branch of mathematical analysis is regarded as the generalization of classical calculus, as it deals with the derivative and integral operators of fractional order. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Some equations include delay effects of finite, infinite, or state-dependent nature. Others are subject to impulsive effect which may be fixed or non-instantaneous. The tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. All the abstract results are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences. Introduces notation, definitions, and foundational concepts of fractional q-calculus Presents existence and attractivity results for a class of implicit fractional q-difference equations in Banach and Fréchet spaces Focuses on the study of a class of coupled systems of Hilfer and Hilfer-Hadamard fractional differential equations
Author: Kolade M. Owolabi
Publisher: Springer Nature
ISBN: 9811500983
Category : Mathematics
Languages : en
Pages : 338
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Book Description
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.
