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Special Functions Fractional Calculus And The Pathway For Entropy
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Book Synopsis Special Functions: Fractional Calculus and the Pathway for Entropy by : Hans J. Haubold
Download or read book Special Functions: Fractional Calculus and the Pathway for Entropy written by Hans J. Haubold and published by MDPI. This book was released on 2018-03-23 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Special Functions: Fractional Calculus and the Pathway for Entropy Dedicated to Professor Dr. A.M. Mathai on the occasion of his 80th Birthday" that was published in Axioms
Book Synopsis Erdélyi–Kober Fractional Calculus by : A. M. Mathai
Download or read book Erdélyi–Kober Fractional Calculus written by A. M. Mathai and published by Springer. This book was released on 2018-09-06 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Erdélyi–Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. The new statistical perspective of Erdélyi–Kober fractional operators outlined in this book will have fundamental applications in the theory of anomalous reaction and diffusion processes dealt with in physics. A major mathematical objective of this book is specifically to examine a new definition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover multivariable cases as well as matrix variable cases. In the matrix variable case, M-convolutions of products and ratios will be used to extend the ideas. We then give a definition for the case of real-valued scalar functions of several matrices.
Book Synopsis Special Functions Of Fractional Calculus: Applications To Diffusion And Random Search Processes by : Trifce Sandev
Download or read book Special Functions Of Fractional Calculus: Applications To Diffusion And Random Search Processes written by Trifce Sandev and published by World Scientific. This book was released on 2022-10-07 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.
Author :Hari M. Srivastava Publisher :World Scientific Publishing Company ISBN 13 :9789814551106 Total Pages :300 pages Book Rating :4.5/5 (511 download)
Book Synopsis Special Functions in Fractional Calculus and Related Fractional Differintegral Equations by : Hari M. Srivastava
Download or read book Special Functions in Fractional Calculus and Related Fractional Differintegral Equations written by Hari M. Srivastava and published by World Scientific Publishing Company. This book was released on 2014-08-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. It does indeed provide several potentially useful tools for solving differential, integral and differintegral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. Many books and monographs (and conference proceedings) deal with the subject of fractional calculus and its applications. However, to the best of our knowledge, there does not exist an exclusive work that co-ordinates the disciplines of fractional calculus and special functions in a potentially useful manner. This book is an attempt in that direction and would serve a dual purpose: in providing key formulas and identities involving special functions and also in opening up some novel avenues of applications of fractional calculus.
Book Synopsis Advances in Special Functions of Fractional Calculus by : Praveen Agarwal; Shilpi
Download or read book Advances in Special Functions of Fractional Calculus written by Praveen Agarwal; Shilpi and published by . This book was released on 2023-04-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, special functions have been developed and applied in a variety of fields, such as combinatorics, astronomy, applied mathematics, physics, and engineering due to their remarkable properties. This volume expands our understanding of special functions by highlighting recent trends in numerical analysis. Interesting applications of special functions and partial differential equations are demonstrated by 15 chapters. Many chapters highlight the importance of numerical techniques and the results of complex analysis. Contributions in the book emphasize the mathematical treatment of questions arising in natural sciences and engineering, particularly those that involve novel problems and their solutions. This volume is a timely update for mathematicians and researchers interested in advanced numerical methods and computational techniques used to solve complex problems List of Chapters 1. Modified Adaptive Synchronization and Anti Synchronization method for Fractional order chaotic systems with uncertain parameters 2. Improved generalized differential transform method for a class of linear non homogeneous ordinary fractional differential equation 3. Incomplete K2-Function 4. Some Results On Incomplete Hypergeometric Functions 5. Transcendental Bernstein Series: Interpolation and Approximation 6. Some Sufficient Conditions For Uniform Convexity Of Normalized 1F2 Function 7. From Abel continuity theorem to Paley-Wiener theorem... 8. A New Class of Truncated Exponential-Gould-Hopper basedGenocchi Polynomials 9. Computational preconditioned Gauss-Seidel via half-sweep approximation to Caputo's time fractional differential equations 10. Krasnoselskii-type Theorems for Monotone Operators in Ordered Banach Algebra with Applications in Fractional Differential Equations and Inclusion 11. General fractional order quadratic functional integral equations: Existence, properties of solutions and some of its Applications 12.Nonlinear set-valued delay functional integral equations of Volterra-Stieltjes type: Existence of solutions, continuous dependence and applications 13.Certain Saigo Fractional Derivatives Of Extended Hypergeometric Functions 14. Some Erdelyi-kober Fractional Integrals Of The Extended Hypergeometric Functions 15. On solutions of Kinetic Model by Sumudu transform
Book Synopsis Fractional and Multivariable Calculus by : A.M. Mathai
Download or read book Fractional and Multivariable Calculus written by A.M. Mathai and published by Springer. This book was released on 2017-07-25 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three discusses deterministic/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined. Chapter four covers non-deterministic/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss–Markov theorem, quadratic forms, and generalized inverses of matrices are covered. Pathway, symmetric, and asymmetric models are covered in chapter six, the concepts are illustrated with graphs.
Book Synopsis Fixed Point Theory and Fractional Calculus by : Pradip Debnath
Download or read book Fixed Point Theory and Fractional Calculus written by Pradip Debnath and published by Springer Nature. This book was released on 2022-05-10 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.
Author :H. M. Srivastava Publisher :Chichester : Ellis Horwood ; New York ; Toronto : Halsted Press ISBN 13 : Total Pages :416 pages Book Rating :4.3/5 (91 download)
Book Synopsis Univalent Functions, Fractional Calculus, and Their Applications by : H. M. Srivastava
Download or read book Univalent Functions, Fractional Calculus, and Their Applications written by H. M. Srivastava and published by Chichester : Ellis Horwood ; New York ; Toronto : Halsted Press. This book was released on 1989 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fractional Differential Equations by : Anatoly Kochubei
Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book 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.
Book Synopsis Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems by : Yeliz Karaca
Download or read book Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems written by Yeliz Karaca and published by Academic Press. This book was released on 2022-06-22 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.
Book Synopsis A Handbook of Generalized Special Functions for Statistical and Physical Sciences by : A. M. Mathai
Download or read book A Handbook of Generalized Special Functions for Statistical and Physical Sciences written by A. M. Mathai and published by Oxford University Press, USA. This book was released on 1993 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complicated generalized special functions such as Meijer's G-functions and functions of matrix arguments are here presented at a level suitable for every potential user. This handbook is thus a valuable reference source and a manual for researchers and advanced students in mathematical statistics, mathematical physics, several branches of mathematics, engineering problems, econometrics, and various applied areas where transcendental functions are used.
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.
Download or read book The H-Function written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2009-10-10 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
Book Synopsis Probability and Statistics by : Arak M. Mathai
Download or read book Probability and Statistics written by Arak M. Mathai and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-12-18 with total page 879 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to concepts of probability theory, probability distributions relevant in the applied sciences, as well as basics of sampling distributions, estimation and hypothesis testing. As a companion for classes for engineers and scientists, the book also covers applied topics such as model building and experiment design. Contents Random phenomena Probability Random variables Expected values Commonly used discrete distributions Commonly used density functions Joint distributions Some multivariate distributions Collection of random variables Sampling distributions Estimation Interval estimation Tests of statistical hypotheses Model building and regression Design of experiments and analysis of variance Questions and answers
Book Synopsis Transfer Entropy by : Deniz Gençağa (Ed.)
Download or read book Transfer Entropy written by Deniz Gençağa (Ed.) and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hurdles for Phage Therapy (PT) to Become a Reality by : Harald Brüssow
Download or read book Hurdles for Phage Therapy (PT) to Become a Reality written by Harald Brüssow and published by MDPI. This book was released on 2019-08-20 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alternative treatment modes for antibiotic-resistant bacterial pathogens have become a public health priority. Bacteriophages are bacterial viruses that infect and lyse bacterial cells. Since bacteriophages are frequently bacterial host species-specific and can often also infect antibiotic-resistant bacterial cells, they could represent ideal antimicrobials for fighting the antibiotic resistance crisis. The medical use of bacteriophages has become known as phage therapy. It is widely used in Russia, where phage cocktails are sold in pharmacies as an over-the-counter drug. However, no phage product has been registered for medical purposes outside of the former Soviet Union. The current Special Issue of Viruses contains a collection of papers from opinion leaders in the field who explore hurdles to the introduction of phage therapy in western countries. The articles cover diverse topics ranging from patent to regulatory issues, the targeting of suitable bacterial infections, and the selection and characterization of safe and efficient phage cocktails. Phage resistance is discussed, and gaps in our knowledge of phage–bacterium interactions in the mammalian body are revealed, while other articles explore the use of phages in food production and processing.
Book Synopsis Orthogonal Polynomials and Special Functions by : Richard Askey
Download or read book Orthogonal Polynomials and Special Functions written by Richard Askey and published by SIAM. This book was released on 1975-06-01 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.
