Applications In Physics Part B
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Basic Theory
Author: Anatoly Kochubei
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2019-02-19
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.
Supercomputing, Collision Processes, and Applications
Author: Kenneth L. Bell
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-04-18
Professor Philip G. Burke, CBE, FRS formally retired on 30 September 1998. To recognise this occasion some of his colleagues, friends, and former students decided to hold a conference in his honour and to present this volume as a dedication to his enormous contribution to the theoretical atomic physics community. The conference and this volume of the invited talks reflect very closely those areas with which he has mostly been asso- ated and his influence internationally on the development of atomic physics coupled with a parallel growth in supercomputing. Phil’s wide range of interests include electron-atom/molecule collisions, scattering of photons and electrons by molecules adsorbed on surfaces, collisions involving oriented and chiral molecules, and the development of non-perturbative methods for studying multiphoton processes. His devel- ment of the theory associated with such processes has enabled important advances to be made in our understanding of the associated physics, the interpretation of experimental data, has been invaluable in application to fusion processes, and the study of astrophysical plasmas (observed by both ground- and space-based telescopes). We therefore offer this volume as our token of affection and respect to Philip G. Burke, with the hope that it may also fill a gap in the literature in these important fields.
Mathematical Economics
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.