Mathematical models of the volumetric deformation of rock materials based on fractional calculus theory

2021 ◽  
Vol 14 (24) ◽  
Author(s):  
Mingming He ◽  
Zhiqiang Zhang ◽  
Ning Li
Keyword(s):  
Fractional Calculus ◽  
Mathematical Models ◽  
Rock Materials ◽  
Volumetric Deformation

scholarly journals Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chun-Ying Long ◽  
Yang Zhao ◽  
Hossein Jafari
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Mathematical Models ◽  
Cantor Sets ◽  
Forest Gap ◽  
Local Fractional Derivative ◽  
Local Fractional Calculus ◽  
Growth Equations ◽  
Gap Models ◽  
Individual Trees

The forest new gap models via local fractional calculus are investigated. The JABOWA and FORSKA models are extended to deal with the growth of individual trees defined on Cantor sets. The local fractional growth equations with local fractional derivative and difference are discussed. Our results are first attempted to show the key roles for the nondifferentiable growth of individual trees.

scholarly journals Description of selected pneumatic elements and systems using fractional calculus

2019 ◽  
Vol 1 (1) ◽  
pp. 43-49
Author(s):  
Daniel Pietruszczak ◽  
Artur Nowocień
Keyword(s):  
Computer Simulation ◽  
Transfer Function ◽  
Fractional Calculus ◽  
Mathematical Models ◽  
Dynamic Systems ◽  
Simulation Research ◽  
Integer Order ◽  
Frequency Domains ◽  
Model Transfer ◽  
Definition Of

The paper presents the application of fractional calculus to describe the dynamics of selected pneumatic elements and systems. In the construction of mathematical models of the analysed dynamic systems, the Riemann-Liouville definition of differintegral of non- integer order was used. For the analysed model,  transfer function of integer  and non-integer order was determined. Functions describing characteristics in frequency domains were determined,  whereas the characteristics of the elements and systems were obtained by means of computer simulation. MATLAB programme were used for the simulation research.

Modeling of Electrochemical Double Layer Capacitors by Means of Fractional Impedance

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Rodolfo Martín ◽  
Jose J. Quintana ◽  
Alejandro Ramos ◽  
Ignacio de la Nuez
Keyword(s):  
Experimental Data ◽  
Impedance Spectroscopy ◽  
Fractional Calculus ◽  
Mathematical Models ◽  
Double Layer ◽  
Frequency Interval ◽  
Minimal Error ◽  
Electrochemical Double Layer Capacitors ◽  
Electrochemical Double Layer ◽  
Double Layer Capacitors

The application of the fractional calculus for modeling electrochemical double layer capacitors is a novel way to get simpler and precise models. On using the impedance spectroscopy method, experimental results for different values have been obtained. In this paper, several classical mathematical models are studied and a different method is introduced in order to get a model from electrochemical double layer capacitors. This method is based on distinct models with fractional elements, and some parameters of the models are fitted to the experimental data, with minimal error. Finally, a Havriliak–Negami function based model is proposed. It achieves excellent fitting to the whole frequency interval analyzed.

Modeling of Electrochemical Double Layer Capacitors by Means of Fractional Impedance

2007 ◽  
Author(s):  
Rodolfo Marti´n ◽  
Jose J. Quintana ◽  
Alejandro Ramos ◽  
Ignacio de la Nuez
Keyword(s):  
Experimental Data ◽  
Impedance Spectroscopy ◽  
Fractional Calculus ◽  
Mathematical Models ◽  
Double Layer ◽  
Experimental Results ◽  
Minimal Error ◽  
Electrochemical Double Layer Capacitors ◽  
Electrochemical Double Layer ◽  
Double Layer Capacitors

The application of the fractional calculus for modeling electrochemical double layer capacitors is a novel way to get simpler and precise models. By means of the method of impedance spectroscopy, experimental results for different values of these have been obtained. In this paper several classical mathematical models are studied and a different method is introduced in order to get a model from electrochemical double layer capacitors. This method is based on distinct models with fractional elements and the fitted of experimental data is realized with few parameters and minimal error. Finally, is proposed a model based in Havriliak-Negami function which achieves an excellent fitted on the over-all frequencies analyzed.

Handbook of Mathematical Models for Languages and Computation

2019 ◽  
Author(s):  
Alexander Meduna ◽  
Petr Horacek ◽  
Martin Tomko
Keyword(s):  
Mathematical Models
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