scholarly journals Combining Fractional Order Derivative and Spectral Variable Selection for Organic Matter Estimation of Homogeneous Soil Samples by VIS–NIR Spectroscopy

2018 ◽  
Vol 10 (3) ◽  
pp. 479 ◽  
Author(s):  
Yongsheng Hong ◽  
Yiyun Chen ◽  
Lei Yu ◽  
Yanfang Liu ◽  
Yaolin Liu ◽  
...  
Keyword(s):  
Organic Matter ◽  
Variable Selection ◽  
Fractional Order ◽  
Nir Spectroscopy ◽  
Soil Samples ◽  
Order Derivative ◽  
Fractional Order Derivative ◽  
Spectral Variable ◽  
Homogeneous Soil ◽  
Selection For

scholarly journals ESTIMATION OF SOIL HEAVY METAL COMBINING FRACTIONAL ORDER DERIVATIVE

2020 ◽  
Vol XLIII-B3-2020 ◽  
pp. 1439-1444
Author(s):  
L. Chen ◽  
K. Tan
Keyword(s):  
Heavy Metal ◽  
Fractional Order ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Order Derivative ◽  
Least Squares Regression ◽  
Estimation Model ◽  
Fractional Order Derivative ◽  
Soil Heavy Metal ◽  
Xuzhou City

Abstract. It is important for the sustainable development of soil and monitoring the soil quality to obtain the heavy metal contents. Visible and near-infrared (Vis–NIR) spectroscopy provides an alternative method for soil heavy metal estimation. A total of 80 soil samples collected in Xuzhou city of China were utilized as data sets for calibration and validation to establish the relationship between the soil reflectance and soil heavy metal content. To amplify the weak spectral characteristic, improve the estimation ability, and explore the characteristic band regions, the preprocessing method of fractional order derivative (FOD) (intervals of 0.25, range of 0–2) and the wavebands selection method of interval partial least squares regression (IPLS) are introduced in this paper. Combining these two methods, for Chromium (Cr), the best estimation model yields Rp2 and RMSRp values of 0.97 and 2.20, respectively, when fractional order is 0.5. This paper explores the potential that FOD conducts the most appropriate order to preprocess spectra and IPLS selects the feature band regions in estimating soil heavy metal of Cr. The results show that FOD and IPLS can strengthen the soil information and improve the accuracy and stability of soil heavy metal estimation effectively.

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 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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