scholarly journals An asymptotic fractional differential model of spherical flame

1998 ◽  
Vol 5 ◽  
pp. 15-27 ◽  
Author(s):  
Jacques Audounet ◽  
Jean-Michel Roquejoffre
Keyword(s):  
Differential Model ◽  
Spherical Flame ◽  
Fractional Differential

Fractional Differential Model of Resonant Transfer of Excitations in Plasma

2018 ◽  
Vol 61 (9) ◽  
pp. 1551-1558
Author(s):  
V. V. Uchaikin ◽  
E. V. Kozhemyakina
Keyword(s):  
Differential Model ◽  
Fractional Differential

Response spectra generation using a fractional differential model

2018 ◽  
Vol 115 ◽  
pp. 719-729 ◽  
Author(s):  
Armando Hermosillo-Arteaga ◽  
Miguel P. Romo ◽  
Roberto Magaña-del-Toro
Keyword(s):  
Response Spectra ◽  
Differential Model ◽  
Fractional Differential

The Adaptive Fractional Order Differential Model for Image Enhancement Based on Segmentation

2017 ◽  
Vol 32 (03) ◽  
pp. 1854005 ◽  
Author(s):  
Suqin Chen ◽  
Fengqun Zhao
Keyword(s):  
Image Enhancement ◽  
Fractional Order ◽  
Target Object ◽  
Optimal Order ◽  
Enhancement Effect ◽  
Differential Model ◽  
Enhancement Method ◽  
Fractional Differential ◽  
Object Area ◽  
Different Characteristics

For image enhancement method based on the fractional order differential, it is difficult to artificially give the optimal order of the fractional differential which can make the image enhancement effect better, and it is hard to ensure the enhancement of the target object while preserving the information of background pixels if the entire image is filtered by a fixed differential order. In order to solve this problem, the image is segmented into the object area and the background area according to the Otsu threshold algorithm based on Markov Random Field firstly. On the basis of the principle of the fractional differential for image enhancement, a piecewise function is established by combining with the different characteristics of pixels in each area, then the best order of fractional differential in the two areas can be determined adaptively. Thus, a novel adaptive fractional order differential algorithm for image enhancement on the basis of segmentation is put forward. Several fog-degraded traffic images are selected for experiments and processed by three other algorithms. The results of comparison exhibit the superiority of our algorithm.

scholarly journals On the selection of fractional-differential model of convective diffusion with mass exchange

2020 ◽  
pp. 7-10
Author(s):  
Vsevolod Bohaienko ◽  
Anatolij Gladky
Keyword(s):  
Decision Making ◽  
Mass Exchange ◽  
Caputo Derivative ◽  
Heuristic Algorithms ◽  
Convective Diffusion ◽  
Concentration Field ◽  
Model Parameters ◽  
Differential Model ◽  
Fractional Differential

The paper considers two fractional-differential models of convective diffusion with mass exchange and proposes a decision-making algorithm for determining the optimal model at the time of concentration field observation. As for soils of fractal structure, direct experimental determination of model parameters’ values and type of mass exchange process is in many cases impossible, calibration and determination of the most adequate models is performed mainly solving inverse problems by, in particular, meta-heuristic algorithms that are computationally complex. In order to reduce the computational complexity, we study the qualitative differences between diffusion processes described by fractional-differential models with non-local mass exchange on the base of the Caputo derivative and local non-linear mass exchange based on the non-equilibrium sorption equation that corresponds to the description by the Caputo-Fabrizio derivative. We determine under which conditions both models within a given accuracy describe the same set of measurements at a certain moment of time. When the solutions are close at a certain initial stage of process development, the model with the Caputo derivative describes its faster approach to a steady state. Based on the obtained estimates of differences in solutions, a decision-making algorithm is proposed to determine the most accurate model and the values of its parameters concurrently with the acquisition of measurements. This algorithm’s usage reduces the time spent on solving inverse calibration problems.

scholarly journals The Fractional Differential Model of HIV-1 Infection of CD4+T-Cells with Description of the Effect of Antiviral Drug Treatment

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Bijan Hasani Lichae ◽  
Jafar Biazar ◽  
Zainab Ayati
Keyword(s):  
T Cells ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Antiviral Drug ◽  
Adomian Decomposition Method ◽  
Differential Model ◽  
Proposed Model ◽  
Adomian Decomposition ◽  
Fractional Differential ◽  
Hiv 1

In this paper, the fractional-order differential model of HIV-1 infection of CD4+T-cells with the effect of drug therapy has been introduced. There are three components: uninfected CD4+T-cells,x, infected CD4+T-cells,y, and density of virions in plasma,z. The aim is to gain numerical solution of this fractional-order HIV-1 model by Laplace Adomian decomposition method (LADM). The solution of the proposed model has been achieved in a series form. Moreover, to illustrate the ability and efficiency of the proposed approach, the solution will be compared with the solutions of some other numerical methods. The Caputo sense has been used for fractional derivatives.

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