A new collection of real world applications of fractional calculus in science and engineering

2018 ◽  
Vol 64 ◽  
pp. 213-231 ◽  
Author(s):  
HongGuang Sun ◽  
Yong Zhang ◽  
Dumitru Baleanu ◽  
Wen Chen ◽  
YangQuan Chen
Keyword(s):  
Fractional Calculus ◽  
Real World ◽  
Science And Engineering ◽  
Real World Applications

scholarly journals Applications of Distributed-Order Fractional Operators: A Review

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 110
Author(s):  
Wei Ding ◽  
Sansit Patnaik ◽  
Sai Sidhardh ◽  
Fabio Semperlotti
Keyword(s):  
Fractional Calculus ◽  
Real World ◽  
Transport Processes ◽  
Model Systems ◽  
Variable Order ◽  
Fractional Operators ◽  
Research Activity ◽  
Road Map ◽  
Real World Applications ◽  
Distributed Order

Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

scholarly journals RSCS: A Parallel Simplex Algorithm for the Nimrod/O Optimization Toolset

2006 ◽  
Vol 14 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Andrew Lewis ◽  
David Abramson ◽  
Tom Peachey
Keyword(s):  
Real World ◽  
Search Algorithm ◽  
Simplex Algorithm ◽  
General Purpose ◽  
Parallel And Distributed Computing ◽  
Science And Engineering ◽  
Original Algorithm ◽  
Real World Applications ◽  
Local Gradient ◽  
Nelder Mead Algorithm

This paper describes a method of parallelisation of the popular Nelder-Mead simplex optimization algorithms that can lead to enhanced performance on parallel and distributed computing resources. A reducing set of simplex vertices are used to derive search directions generally closely aligned with the local gradient. When tested on a range of problems drawn from real-world applications in science and engineering, this reducing set concurrent simplex (RSCS) variant of the Nelder-Mead algorithm compared favourably with the original algorithm, and also with the inherently parallel multidirectional search algorithm (MDS). All algorithms were implemented and tested in a general-purpose, grid-enabled optimization toolset.

Role of Artificial Intelligence (AI) in Thermal Science and Engineering

2007 ◽  
Author(s):  
Kwang-Tzu Yang
Keyword(s):  
Artificial Intelligence ◽  
Real World ◽  
Science And Engineering ◽  
Recent Advances ◽  
Real World Applications ◽  
Critical Problems

The use of artificial intelligence methodologies in a variety of real-world applications has been around for some time. However, the application of such methodologies to thermal science and engineering is relatively new, but is receiving ever-increasing attention in the published literature since the mid 1990s. Such attention is due essentially to special requirements and needs of the field of thermal science and Engineering (TSE) in terms of its increasing complexity and the recognition that it is not feasible to approach many critical problems in this field by the use of traditional analysis. The purpose of the present brief review is to point out the recent advances in the artificial intelligence (AI) field and the successes of such methodologies to the current problems in thermal science and engineering. Some shortfalls and prospect for future applications will also be indicated.

scholarly journals Editorial for Special Issue “Fractional Calculus and Special Functions with Applications”

2021 ◽  
Vol 5 (4) ◽  
pp. 224
Author(s):  
Mehmet Ali Özarslan ◽  
Arran Fernandez ◽  
Iván Area
Keyword(s):  
Fractional Calculus ◽  
Real World ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Fractional Integrals ◽  
Special Issue ◽  
Integer Order ◽  
Real World Applications

The study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications due to their properties of interpolation between operators of integer order [...]

scholarly journals Electronic Phenomena of Transition Metal Oxides

Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 256
Author(s):  
Christian Rodenbücher ◽  
Kristof Szot
Keyword(s):  
Solid State ◽  
Transition Metal ◽  
Metal Oxides ◽  
Real World ◽  
Transition Metal Oxides ◽  
Major Research ◽  
Research Fields ◽  
Real World Applications

Transition metal oxides with ABO3 or BO2 structures have become one of the major research fields in solid state science, as they exhibit an impressive variety of unusual and exotic phenomena with potential for their exploitation in real-world applications [...]

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