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

HG Sun, Y Zhang, D Baleanu, W Chen… - … in Nonlinear Science and …, 2018 - Elsevier
Fractional calculus is at this stage an arena where many models are still to be introduced,
discussed and applied to real world applications in many branches of science and …

The role of fractional calculus in modeling biological phenomena: A review

C Ionescu, A Lopes, D Copot, JAT Machado… - … in Nonlinear Science …, 2017 - Elsevier
This review provides the latest developments and trends in the application of fractional
calculus (FC) in biomedicine and biology. Nature has often showed to follow rather simple …

Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system

D Baleanu, SS Sajjadi, JH Asad, A Jajarmi… - Advances in Difference …, 2021 - Springer
In this paper, the hyperchaos analysis, optimal control, and synchronization of a
nonautonomous cardiac conduction system are investigated. We mainly analyze, control …

[图书][B] General fractional derivatives: theory, methods and applications

XJ Yang - 2019 - taylorfrancis.com
General Fractional Derivatives: Theory, Methods and Applications provides knowledge of
the special functions with respect to another function, and the integro-differential operators …

Review of fractional PID controller

P Shah, S Agashe - Mechatronics, 2016 - Elsevier
Fractional calculus has been studied for over three centuries, and it has multifarious
applications in science and engineering. This review investigates its progress since the first …

Applications of variable-order fractional operators: a review

S Patnaik, JP Hollkamp… - Proceedings of the …, 2020 - royalsocietypublishing.org
Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

[图书][B] Mittag-Leffler functions, related topics and applications

R Gorenflo, AA Kilbas, F Mainardi, SV Rogosin - 2020 - Springer
Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

[图书][B] Basic theory of fractional differential equations

Y Zhou - 2023 - books.google.com
This accessible monograph is devoted to a rapidly developing area on the research of
qualitative theory of fractional ordinary differential equations and evolution equations. It is …

[图书][B] Fractional derivative modeling in mechanics and engineering

W Chen, HG Sun, X Li - 2022 - Springer
Classic Newtonian mechanics assumes that space and time are continuous everywhere.
The basic physical quantities (eg speed, acceleration and force) can be described by an …

[图书][B] General fractional derivatives with applications in viscoelasticity

XJ Yang, F Gao, Y Ju - 2020 - books.google.com
General Fractional Derivatives with Applications in Viscoelasticity introduces the newly
established fractional-order calculus operators involving singular and non-singular kernels …