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Author: Bashir Ahmad Publisher: World Scientific ISBN: 9811224471 Category : Mathematics Languages : en Pages : 468
Book Description
This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
Author: Bashir Ahmad Publisher: World Scientific ISBN: 9811224471 Category : Mathematics Languages : en Pages : 468
Book Description
This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
Author: Johnny Henderson Publisher: Academic Press ISBN: 0128036796 Category : Mathematics Languages : en Pages : 323
Book Description
Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. - Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions - Discusses second order difference equations with multi-point boundary conditions - Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions
Author: Bashir Ahmad Publisher: World Scientific ISBN: 9811230420 Category : Mathematics Languages : en Pages : 597
Book Description
There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain.The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.
Author: Igor Podlubny Publisher: Elsevier ISBN: 0080531989 Category : Mathematics Languages : en Pages : 366
Book Description
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
Author: Alberto Carpinteri Publisher: Springer ISBN: 3709126649 Category : Technology & Engineering Languages : en Pages : 352
Book Description
The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
Author: Saïd Abbas Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110553813 Category : Mathematics Languages : en Pages : 362
Book Description
This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations
Author: Kai Diethelm Publisher: Springer ISBN: 3642145744 Category : Mathematics Languages : en Pages : 251
Book Description
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Author: Anatoly Kochubei Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110571668 Category : Mathematics Languages : en Pages : 528
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 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.
Author: Yong Zhou Publisher: World Scientific ISBN: 9813148187 Category : Mathematics Languages : en Pages : 380
Book Description
This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations. It provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the technique of Picard operators, critical point theory and semigroup theory. Based on the research work carried out by the authors and other experts during the past seven years, the contents are very recent and comprehensive.In this edition, two new topics have been added, that is, fractional impulsive differential equations, and fractional partial differential equations including fractional Navier-Stokes equations and fractional diffusion equations.
Author: Michal Fečkan Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110521555 Category : Mathematics Languages : en Pages : 506
Book Description
This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions
Author: Bashir Ahmad
Author: Bashir Ahmad
Author: Johnny Henderson
Author: Bashir Ahmad
Author: Igor Podlubny
Author: Alberto Carpinteri
Author: Saïd Abbas
Author: Kai Diethelm
Author: Anatoly Kochubei
Author: Yong Zhou
Author: Michal Fečkan