Fractal Calculus And Its Applications: Fα-calculus

Fractal Calculus And Its Applications: Fα-calculus
Author: Alireza Khalili Golmankhaneh
Publisher: World Scientific
Total Pages: 328
Release: 2022-08-29
Genre: Mathematics
ISBN: 9811261121

Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.This book is the first to introduce fractal calculus and provides a basis for the research and development of this framework. It is suitable for undergraduate and graduate students in mathematics and physics who have mastered general mathematics, quantum physics, and statistical mechanics, as well as researchers dealing with fractal structures in various disciplines.

Applications Of Fractional Calculus In Physics

Applications Of Fractional Calculus In Physics
Author: Rudolf Hilfer
Publisher: World Scientific
Total Pages: 473
Release: 2000-03-02
Genre: Science
ISBN: 9814496200

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.

Fractional Dynamics

Fractional Dynamics
Author: Carlo Cattani
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 392
Release: 2015-01-01
Genre: Mathematics
ISBN: 3110472090

The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.

Fractional Differential Equations

Fractional Differential Equations
Author: Anatoly Kochubei
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 528
Release: 2019-02-19
Genre: Mathematics
ISBN: 3110571668

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 Dynamics

Fractional Dynamics
Author: Vasily E. Tarasov
Publisher: Springer Science & Business Media
Total Pages: 504
Release: 2011-01-04
Genre: Science
ISBN: 3642140033

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Special Functions

Special Functions
Author: George E. Andrews
Publisher: Cambridge University Press
Total Pages: 684
Release: 1999
Genre: Mathematics
ISBN: 9780521789882

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Fractal Physiology

Fractal Physiology
Author: James B Bassingthwaighte
Publisher: Springer
Total Pages: 371
Release: 2013-05-27
Genre: Medical
ISBN: 1461475724

I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.

Fractals and Fractional Calculus in Continuum Mechanics

Fractals and Fractional Calculus in Continuum Mechanics
Author: Alberto Carpinteri
Publisher: Springer
Total Pages: 352
Release: 2014-05-04
Genre: Technology & Engineering
ISBN: 3709126649

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.

Mathematical Economics

Mathematical Economics
Author: Vasily E. Tarasov
Publisher: MDPI
Total Pages: 278
Release: 2020-06-03
Genre: Business & Economics
ISBN: 303936118X

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.