Fractional Calculus In Medical And Health Science

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Fractional Calculus in Medical and Health Science

Author : Devendra Kumar
Publisher : CRC Press
ISBN 13 : 1000081818
Total Pages : 265 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Fractional Calculus in Medical and Health Science by : Devendra Kumar

Download or read book Fractional Calculus in Medical and Health Science written by Devendra Kumar and published by CRC Press. This book was released on 2020-07-09 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.

Fractional Calculus in Medical and Health Science

Author : Devendra Kumar
Publisher : CRC Press
ISBN 13 : 1000081850
Total Pages : 153 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Fractional Calculus in Medical and Health Science by : Devendra Kumar

Download or read book Fractional Calculus in Medical and Health Science written by Devendra Kumar and published by CRC Press. This book was released on 2020-07-09 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.

Fractional Calculus: New Applications in Understanding Nonlinear Phenomena

Author : Mehmet Yavuz
Publisher : Bentham Science Publishers
ISBN 13 : 9815051946
Total Pages : 275 pages
Book Rating : 4.8/5 (15 download)

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Book Synopsis Fractional Calculus: New Applications in Understanding Nonlinear Phenomena by : Mehmet Yavuz

Download or read book Fractional Calculus: New Applications in Understanding Nonlinear Phenomena written by Mehmet Yavuz and published by Bentham Science Publishers. This book was released on 2022-12-14 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators.These have been intensively studied formodelling and analysing real-world phenomena. There is now a growing body of research on new methods to understand natural occurrences and tackle different problems. This book presents ten reviews of recent fractional operators split over three sections: 1. Chaotic Systems and Control (covers the Caputo fractional derivative, and a chaotic fractional-order financial system)2. Heat Conduction (covers the Duhamel theorem for time-dependent source terms, and the Cattaneo–Hristov model for oscillatory heat transfer)3. Computational Methods and Their Illustrative Applications (covers mathematical analysis for understanding 5 real-word phenomena: HTLV-1 infection of CD4+ T-cells, traveling waves, rumor-spreading, biochemical reactions, and the computational fluid dynamics of a non-powered floating object navigating in an approach channel) This volume is a resource for researchers in physics, biology, behavioral sciences, and mathematics who are interested in new applications of fractional calculus in the study of nonlinear phenomena.

Special Functions in Fractional Calculus and Engineering

Author : Harendra Singh
Publisher : CRC Press
ISBN 13 : 1000899756
Total Pages : 315 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Special Functions in Fractional Calculus and Engineering by : Harendra Singh

Download or read book Special Functions in Fractional Calculus and Engineering written by Harendra Singh and published by CRC Press. This book was released on 2023-06-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.

Fractional Calculus

Author : Roy Abi Zeid Daou
Publisher : Nova Science Publishers
ISBN 13 : 9781634630023
Total Pages : 0 pages
Book Rating : 4.6/5 (3 download)

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Book Synopsis Fractional Calculus by : Roy Abi Zeid Daou

Download or read book Fractional Calculus written by Roy Abi Zeid Daou and published by Nova Science Publishers. This book was released on 2014-01-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of this two-volume book, presents history, the mathematical modelling and the applications of fractional order systems, and contains mathematical and theoretical studies and research related to this domain. This volume is made up of 11 chapters. The first chapter presents an analysis of the Caputo derivative and the pseudo state representation with the infinite state approach. The second chapter studies the stability of a class of fractional Cauchy problems. The third chapter shows how to solve fractional order differential equations and fractional order partial differential equations using modern matrix algebraic approaches. Following this chapter, chapter four proposes another analytical method to solve differential equations with local fractional derivative operators. Concerning chapter five, it presents the extended Borel transform and its related fractional analysis. After presenting the analytical resolution methods for fractional calculus, chapter six shows the essentials of fractional calculus on discrete settings. The initialisation of such systems is shown in chapter seven. In fact, this chapter presents a generalised application of the Hankel operator for initialisation of fractional order systems. The last four chapters show some new studies and applications of non-integer calculus. In fact, chapter eight presents the fractional reaction-transport equations and evanescent continuous time random walks. Chapter nine shows a novel approach in the exponential integrators for fractional differential equations. Chapter ten presents the non-fragile tuning of fractional order PD controllers for integrating time delay systems. At the end, chapter eleven proposes a discrete finite-dimensional approximation of linear infinite dimensional systems. To sum up, this volume presents a mathematical and theoretical study of fractional calculus along with a stability study and some applications. This volume ends up with some new techniques and methods applied in fractional calculus. This volume will be followed up by a second volume that focuses on the applications of fractional calculus in several engineering domains.

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

Author : Said Abbas
Publisher : World Scientific
ISBN 13 : 981126127X
Total Pages : 326 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Fractional Differential Equations And Inclusions: Classical And Advanced Topics by : Said Abbas

Download or read book Fractional Differential Equations And Inclusions: Classical And Advanced Topics written by Said Abbas and published by World Scientific. This book was released on 2023-02-02 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

Methods of Mathematical Modelling and Computation for Complex Systems

Author : Jagdev Singh
Publisher : Springer Nature
ISBN 13 : 3030771695
Total Pages : 433 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Methods of Mathematical Modelling and Computation for Complex Systems by : Jagdev Singh

Download or read book Methods of Mathematical Modelling and Computation for Complex Systems written by Jagdev Singh and published by Springer Nature. This book was released on 2021-08-26 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.

Fractional Differential Equations

Author : Mouffak Benchohra
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111334384
Total Pages : 336 pages
Book Rating : 4.1/5 (113 download)

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Book Synopsis Fractional Differential Equations by : Mouffak Benchohra

Download or read book Fractional Differential Equations written by Mouffak Benchohra and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-11-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the existence and uniqueness results for various classes of problems with periodic conditions. All of the problems in this book deal with fractional differential equations and some fractional derivatives such as the Riemann-Liouville, Caputo and Hilfer fractional derivatives. Classical fixed point theorems as well as the coincidence degree theory of Mawhin are employed as tools.

Advances in Mathematical Modelling, Applied Analysis and Computation

Author : Jagdev Singh
Publisher : Springer Nature
ISBN 13 : 9811901791
Total Pages : 632 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Advances in Mathematical Modelling, Applied Analysis and Computation by : Jagdev Singh

Download or read book Advances in Mathematical Modelling, Applied Analysis and Computation written by Jagdev Singh and published by Springer Nature. This book was released on 2022-10-13 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a valuable source for graduate students and researchers and provides a comprehensive introduction to recent theories and applications of mathematical modeling and numerical simulation. It includes selected peer-reviewed papers presented at the 4th International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2021), held at JECRC University, Jaipur, India, during August 5–7, 2021. The book is focused on mathematical modeling of various problems arising in science and engineering and new efficient numerical approaches for solving linear nonlinear problems and rigorous mathematical theories, which can be used to analyze different kinds of mathematical models. Applications of mathematical methods in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science, and finance are presented.

Congress on Intelligent Systems

Author : Harish Sharma
Publisher : Springer Nature
ISBN 13 : 9813369841
Total Pages : 801 pages
Book Rating : 4.8/5 (133 download)

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Book Synopsis Congress on Intelligent Systems by : Harish Sharma

Download or read book Congress on Intelligent Systems written by Harish Sharma and published by Springer Nature. This book was released on 2021-06-01 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of selected papers presented at the First Congress on Intelligent Systems (CIS 2020), held in New Delhi, India, during September 5–6, 2020. It includes novel and innovative work from experts, practitioners, scientists, and decision-makers from academia and industry. It covers topics such as Internet of Things, information security, embedded systems, real-time systems, cloud computing, big data analysis, quantum computing, automation systems, bio-inspired intelligence, cognitive systems, cyber physical systems, data analytics, data/web mining, data science, intelligence for security, intelligent decision making systems, intelligent information processing, intelligent transportation, artificial intelligence for machine vision, imaging sensors technology, image segmentation, convolutional neural network, image/video classification, soft computing for machine vision, pattern recognition, human–computer interaction, robotic devices and systems, autonomous vehicles, intelligent control systems, human motor control, game playing, evolutionary algorithms, swarm optimization, neural network, deep learning, supervised learning, unsupervised learning, fuzzy logic, rough sets, computational optimization, and neuro-fuzzy systems.

Numerical Methods for Fractal-Fractional Differential Equations and Engineering

Author : Muhammad Altaf Khan
Publisher : CRC Press
ISBN 13 : 1000874818
Total Pages : 432 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Numerical Methods for Fractal-Fractional Differential Equations and Engineering by : Muhammad Altaf Khan

Download or read book Numerical Methods for Fractal-Fractional Differential Equations and Engineering written by Muhammad Altaf Khan and published by CRC Press. This book was released on 2023-05-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the simulation and modeling of novel chaotic systems within the frame of fractal-fractional operators. The methods used, their convergence, stability, and error analysis are given, and this is the first book to offer mathematical modeling and simulations of chaotic problems with a wide range of fractal-fractional operators, to find solutions. Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling provides details for stability, convergence, and analysis along with numerical methods and their solution procedures for fractal-fractional operators. The book offers applications to chaotic problems and simulations using multiple fractal-fractional operators and concentrates on models that display chaos. The book details how these systems can be predictable for a while and then can appear to become random. Practitioners, engineers, researchers, and senior undergraduate and graduate students from mathematics and engineering disciplines will find this book of interest._

Novel Antibacterial Biomaterials for Medical Applications and Modeling of Drug Release Process

Author : Vesna Mišković-Stanković
Publisher : CRC Press
ISBN 13 : 1040035973
Total Pages : 284 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Novel Antibacterial Biomaterials for Medical Applications and Modeling of Drug Release Process by : Vesna Mišković-Stanković

Download or read book Novel Antibacterial Biomaterials for Medical Applications and Modeling of Drug Release Process written by Vesna Mišković-Stanković and published by CRC Press. This book was released on 2024-06-12 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive review of synthesis and physicochemical and biological characterization of novel antibacterial biomaterials produced according to original procedures and aimed at medical applications such as wound dressing, soft and hard tissue implants, drug delivery devices, and carriers for cell cultivation. It is intended for all researchers working in the fields of biomaterials and biomedical engineering, as well as medical professionals, science and engineering graduate students, academics, and industrial researchers. Includes in-depth discussions on synthesis and physicochemical characterization of novel poly vinyl alcohol-based hydrogels aimed at wound dressings and soft tissue implants Explores synthesis and physicochemical characterization of novel bioceramic hydroxyapatite-based coatings on metal surface aimed for hard tissue implants Reviews cytotoxicity and antibacterial activity of novel poly vinyl alcohol-based hydrogels aimed for wound dressing and soft tissue implants Discusses cytotoxicity and antibacterial activity of bioceramic hydroxyapatite-based coatings on metal surface aimed for hard tissue implants Provides original fractional derivative models of drug release process from hydrogels and bioceramic coatings on metal surface and explores diffusion mechanism

Fractional-Order Design

Author : Ahmed G. Radwan
Publisher : Academic Press
ISBN 13 : 0323902049
Total Pages : 550 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Fractional-Order Design by : Ahmed G. Radwan

Download or read book Fractional-Order Design written by Ahmed G. Radwan and published by Academic Press. This book was released on 2021-10-22 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional-Order Design: Devices, Circuits, and Systems introduces applications from the design perspective so that the reader can learn about, and get ready to, design these applications. The book also includes the different techniques employed to comprehensively and straightforwardly design fractional-order systems/devices. Furthermore, a lot of mathematics is available in the literature for solving the fractional-order calculus for system application. However, a small portion is employed in the design of fractional-order systems. This book introduces the mathematics that has been employed explicitly for fractional-order systems. Students and scholars who wants to quickly understand the field of fractional-order systems and contribute to its different domains and applications will find this book a welcomed resource. Presents a simple and comprehensive understanding of the field of fractional-order systems Offers practical knowledge on the design of fractional-order systems for different applications Exposes users to the possible new areas of applications of fractional-order systems

Functional Fractional Calculus

Author : Shantanu Das
Publisher : Springer Science & Business Media
ISBN 13 : 3642205453
Total Pages : 612 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Functional Fractional Calculus by : Shantanu Das

Download or read book Functional Fractional Calculus written by Shantanu Das and published by Springer Science & Business Media. This book was released on 2011-06-01 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.

Nonlinear Analysis: Problems, Applications and Computational Methods

Author : Zakia Hammouch
Publisher : Springer Nature
ISBN 13 : 3030622991
Total Pages : 249 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Nonlinear Analysis: Problems, Applications and Computational Methods by : Zakia Hammouch

Download or read book Nonlinear Analysis: Problems, Applications and Computational Methods written by Zakia Hammouch and published by Springer Nature. This book was released on 2020-11-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th–9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes various topics including fractional differential systems of various types, time-fractional systems, nonlinear Jerk equations, reproducing kernel Hilbert space method, thrombin receptor activation mechanism model, labour force evolution model, nonsmooth vector optimization problems, anisotropic elliptic nonlinear problem, viscous primitive equations of geophysics, quadratic optimal control problem, multi-orthogonal projections and generalized continued fractions. The conference aimed at fostering cooperation among students, researchers and experts from diverse areas of applied mathematics and related sciences through fruitful deliberations on new research findings. This book is expected to be resourceful for researchers, educators and graduate students interested in applied mathematics and interactions of mathematics with other branches of science and engineering.

Engineering Mathematics and Artificial Intelligence

Author : Herb Kunze
Publisher : CRC Press
ISBN 13 : 1000907899
Total Pages : 717 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Engineering Mathematics and Artificial Intelligence by : Herb Kunze

Download or read book Engineering Mathematics and Artificial Intelligence written by Herb Kunze and published by CRC Press. This book was released on 2023-07-26 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of Artificial Intelligence (AI) and Machine Learning (ML) have grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This book represents a key reference for anybody interested in the intersection between mathematics and AI/ML and provides an overview of the current research streams. Engineering Mathematics and Artificial Intelligence: Foundations, Methods, and Applications discusses the theory behind ML and shows how mathematics can be used in AI. The book illustrates how to improve existing algorithms by using advanced mathematics and offers cutting-edge AI technologies. The book goes on to discuss how ML can support mathematical modeling and how to simulate data by using artificial neural networks. Future integration between ML and complex mathematical techniques is also highlighted within the book. This book is written for researchers, practitioners, engineers, and AI consultants.

Advanced Numerical Methods for Differential Equations

Author : Harendra Singh
Publisher : CRC Press
ISBN 13 : 1000381110
Total Pages : 245 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Advanced Numerical Methods for Differential Equations by : Harendra Singh

Download or read book Advanced Numerical Methods for Differential Equations written by Harendra Singh and published by CRC Press. This book was released on 2021-06-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.