scholarly journals Modelling the Formation of Liver Zones within the Scope of Fractional Order Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Abdon Atangana ◽  
Suares Clovis Oukouomi Noutchie
Keyword(s):  
Hilbert Space ◽  
Mathematical Modelling ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Time Dependent ◽  
Order Derivative ◽  
Stationary States ◽  
Formation Zone ◽  
Iteration Methods ◽  
Time Dependent Solution

We develop and extend earlier results related to mathematical modelling of the liver formation zone by the adoption of noninteger order derivative. The hidden uncertainties in the model are captured and controlled thanks to the Caputo derivative. The stationary states are investigated and the time-dependent solution is approximated using two recent iteration methods. In particular, we discuss the convergence of these methods by constructing a suitable Hilbert space.

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

2020 ◽  
Vol 9 (11) ◽  
pp. 9769-9780
Author(s):  
S.G. Khavale ◽  
K.R. Gaikwad
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Order Derivative ◽  
Laplace Inversion ◽  
State Space Approach ◽  
Spherical Region ◽  
Fractional Order Derivative ◽  
Numerical Laplace Inversion ◽  
Mathcad Software ◽  
Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

scholarly journals Estimating Agricultural Soil Moisture Content through UAV-Based Hyperspectral Images in the Arid Region

2021 ◽  
Vol 13 (8) ◽  
pp. 1562
Author(s):  
Xiangyu Ge ◽  
Jianli Ding ◽  
Xiuliang Jin ◽  
Jingzhe Wang ◽  
Xiangyue Chen ◽  
...  
Keyword(s):  
Data Mining ◽  
Soil Moisture ◽  
Moisture Content ◽  
Hyperspectral Imaging ◽  
Fractional Order ◽  
Arid Regions ◽  
Soil Moisture Content ◽  
Order Derivative ◽  
Imaging Data ◽  
Strategy I

Unmanned aerial vehicle (UAV)-based hyperspectral remote sensing is an important monitoring technology for the soil moisture content (SMC) of agroecological systems in arid regions. This technology develops precision farming and agricultural informatization. However, hyperspectral data are generally used in data mining. In this study, UAV-based hyperspectral imaging data with a resolution o 4 cm and totaling 70 soil samples (0–10 cm) were collected from farmland (2.5 × 104 m2) near Fukang City, Xinjiang Uygur Autonomous Region, China. Four estimation strategies were tested: the original image (strategy I), first- and second-order derivative methods (strategy II), the fractional-order derivative (FOD) technique (strategy III), and the optimal fractional order combined with the optimal multiband indices (strategy IV). These strategies were based on the eXtreme Gradient Boost (XGBoost) algorithm, with the aim of building the best estimation model for agricultural SMC in arid regions. The results demonstrated that FOD technology could effectively mine information (with an absolute maximum correlation coefficient of 0.768). By comparison, strategy IV yielded the best estimates out of the methods tested (R2val = 0.921, RMSEP = 1.943, and RPD = 2.736) for the SMC. The model derived from the order of 0.4 within strategy IV worked relatively well among the different derivative methods (strategy I, II, and III). In conclusion, the combination of FOD technology and the optimal multiband indices generated a highly accurate model within the XGBoost algorithm for SMC estimation. This research provided a promising data mining approach for UAV-based hyperspectral imaging data.

scholarly journals Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

scholarly journals Iterative analysis of non-linear Swift-Hohenberg equations under nonsingular fractional order derivative

2021 ◽  
pp. 104080
Author(s):  
Israr Ahmad ◽  
Thabet Abdeljawad ◽  
Ibrahim Mahariq ◽  
Kamal Shah ◽  
Nabil Mlaiki ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order Derivative ◽  
Fractional Order Derivative ◽  
Iterative Analysis ◽  
Non Linear
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