Productivity with Fatigue and Long Memory: Fractional Calculus Approach

Tarasova, Valentina V.

doi:10.1007/s40819-019-0599-x

Cited by 3 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…energy systems [4], and quantum systems [5]; in biology, modeling in cell biology [6], cancer biology [7], and computational biology [8,9]; in engineering, dynamics and control [10,11], fluid mechanics and aerodynamics [12,13], and telecommunication [14,15]. These are some areas where fractional calculus is applied.…”

Section: Introductionmentioning

confidence: 99%

FPGA Implementation of Parameter-Switching Scheme to Stabilize Chaos in Fractional Spherical Systems and Usage in Secure Image Transmission

et al. 2023

View full text Add to dashboard Cite

The main objective of this work was to implement the parameter-switching chaos control scheme for fractional-order spherical systems and develop a chaos-based image encryption and transmission system. The novelty in the developed secure communication system is the application of the parameter-switching scheme in the decryption of RGB and grayscale images, which undergo one round of encryption using the chaotic states of the fractional system and a diffusion process. The secure communication system has a synchronized master and slave topology, resulting in transmitter and receiver systems for encrypting and decrypting images, respectively. This work was demonstrated numerically and also implemented on two FPGAs, namely Artix-7 AC701 and Cyclone V. The results show that the parameter-switching scheme controls chaos in the fractional-order spherical systems effectively. Furthermore, the performance analysis of the image encryption and transmission system shows that there is no similarity between the original and encrypted images, while the decryption of the encrypted images is without a loss of quality. The best result in terms of the encryption was obtained from the chaotic state x of the fractional-order system, with correlation coefficients of 0.0511 and 0.0392 for the RGB and grayscale images, respectively. Finally, the utilization of the FPGA logical resources shows that the implementation on Artix-7 AC701 is more logic-efficient than on Cyclone V.

show abstract

Section: Introductionmentioning

confidence: 99%

FPGA Implementation of Parameter-Switching Scheme to Stabilize Chaos in Fractional Spherical Systems and Usage in Secure Image Transmission

et al. 2023

View full text Add to dashboard Cite

show abstract

Extended Reality (XR) Applications in Architectural Practice: Towards a Development Framework

Abhari

Drinkwine

et al. 2021

Lecture Notes in Computer Science

View full text Add to dashboard Cite

On History of Mathematical Economics: Application of Fractional Calculus

Tarasov

2019

Mathematics

182

View full text Add to dashboard Cite

Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe economic phenomena, effects, and processes. At the present moment the new revolution, which can be called “Memory revolution”, is actually taking place in modern economics. This revolution is intended to “cure amnesia” of modern economic theory, which is caused by the use of differential and integral operators of integer orders. In economics, the description of economic processes should take into account that the behavior of economic agents may depend on the history of previous changes in economy. The main mathematical tool designed to “cure amnesia” in economics is fractional calculus that is a theory of integrals, derivatives, sums, and differences of non-integer orders. This paper contains a brief review of the history of applications of fractional calculus in modern mathematical economics and economic theory. The first stage of the Memory Revolution in economics is associated with the works published in 1966 and 1980 by Clive W. J. Granger, who received the Nobel Memorial Prize in Economic Sciences in 2003. We divide the history of the application of fractional calculus in economics into the following five stages of development (approaches): ARFIMA; fractional Brownian motion; econophysics; deterministic chaos; mathematical economics. The modern stage (mathematical economics) of the Memory revolution is intended to include in the modern economic theory new economic concepts and notions that allow us to take into account the presence of memory in economic processes. The current stage actually absorbs the Granger approach based on ARFIMA models that used only the Granger–Joyeux–Hosking fractional differencing and integrating, which really are the well-known Grunwald–Letnikov fractional differences. The modern stage can also absorb other approaches by formulation of new economic notions, concepts, effects, phenomena, and principles. Some comments on possible future directions for development of the fractional mathematical economics are proposed.

show abstract

Productivity with Fatigue and Long Memory: Fractional Calculus Approach

Cited by 3 publications

References 25 publications

FPGA Implementation of Parameter-Switching Scheme to Stabilize Chaos in Fractional Spherical Systems and Usage in Secure Image Transmission

FPGA Implementation of Parameter-Switching Scheme to Stabilize Chaos in Fractional Spherical Systems and Usage in Secure Image Transmission

Extended Reality (XR) Applications in Architectural Practice: Towards a Development Framework

On History of Mathematical Economics: Application of Fractional Calculus

Contact Info

Product

Resources

About