Applications in Engineering, Life and Social Sciences, Part A
Applications in Engineering, Life and Social Sciences, Part A

Author: Dumitru Bǎleanu

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-04-01

Total Pages: 352

ISBN-13: 3110570963

DOWNLOAD EBOOK

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 seventh volume collects authoritative chapters covering several applications of fractional calculus in in engineering, life, and social sciences, including applications in biology and medicine, mechanics of complex media, economy, and electrical devices.

Applications in Engineering, Life and Social Sciences, Part B
Applications in Engineering, Life and Social Sciences, Part B

Author: Dumitru Bǎleanu

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-04-01

Total Pages: 292

ISBN-13: 3110571927

DOWNLOAD EBOOK

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 eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.

Mathematical Economics
Mathematical Economics

Author: Vasily E. Tarasov

Publisher: MDPI

Published: 2020-06-03

Total Pages: 278

ISBN-13: 303936118X

DOWNLOAD EBOOK

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

Fractional Integrals and Derivatives: “True” versus “False”
Fractional Integrals and Derivatives: “True” versus “False”

Author: Yuri Luchko

Publisher: MDPI

Published: 2021-03-16

Total Pages: 280

ISBN-13: 303650494X

DOWNLOAD EBOOK

This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.

Basic Theory
Basic Theory

Author: Anatoly Kochubei

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-02-19

Total Pages: 490

ISBN-13: 3110571625

DOWNLOAD EBOOK

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
Numerical Methods

Author: George Em Karniadakis

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-04-15

Total Pages: 360

ISBN-13: 3110571684

DOWNLOAD EBOOK

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 third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.

Fixed Point Theory and Fractional Calculus
Fixed Point Theory and Fractional Calculus

Author: Pradip Debnath

Publisher: Springer Nature

Published: 2022-05-10

Total Pages: 358

ISBN-13: 9811906688

DOWNLOAD EBOOK

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.

Fractional Differential Equations
Fractional Differential Equations

Author: Anatoly Kochubei

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-02-19

Total Pages: 528

ISBN-13: 3110571668

DOWNLOAD EBOOK

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.

Fractional Differential Equations
Fractional Differential Equations

Author: Mouffak Benchohra

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-11-20

Total Pages: 336

ISBN-13: 3111334384

DOWNLOAD EBOOK

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.