scholarly journals Impact of Fractional Calculus on Correlation Coefficient between Available Potassium and Spectrum Data in Ground Hyperspectral and Landsat 8 Image

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 488 ◽  
Author(s):  
Chengbiao Fu ◽  
Shu Gan ◽  
Xiping Yuan ◽  
Heigang Xiong ◽  
Anhong Tian
Keyword(s):  
Correlation Coefficient ◽  
Fractional Order ◽  
Saline Soil ◽  
Hyperspectral Data ◽  
Potassium Content ◽  
Landsat 8 ◽  
Data Pretreatment ◽  
Spectral Transformations ◽  
Fractional Differential ◽  
New Perspective

As the level of potassium can interfere with the normal circulation process of biosphere materials, the available potassium is an important index to measure the ability of soil to supply potassium to crops. There are rarely studies on the inversion of available potassium content using ground hyperspectral remote sensing and Landsat 8 multispectral satellite data. Pretreatment of saline soil field hyperspectral data based on fractional differential has rarely been reported, and the corresponding relationship between spectrum and available potassium content has not yet been reported. Because traditional integer-order differential preprocessing methods ignore important spectral information at fractional-order, it is easy to reduce the accuracy of inversion model. This paper explores spectral preprocessing effect based on Grünwald–Letnikov fractional differential (order interval is 0.2) between zero-order and second-order. Field spectra of saline soil were collected in Fukang City of Xinjiang. The maximum absolute of correlation coefficient between ground hyperspectral reflectance and available potassium content for five mathematical transformations appears in the fractional-order. We also studied the tendency of correlation coefficient under different fractional-order based on seven bands corresponding to the Landsat 8 image. We found that fractional derivative can significantly improve the correlation, and the maximum absolute of correlation coefficient under five spectral transformations is in Band 2, which is 0.715766 for the band at 467 nm. This study deeply mined the potential information of spectra and made up for the gap of fractional differential for field hyperspectral data, providing a new perspective for field hyperspectral technology to monitor the content of soil available potassium.

Effect of Fractional Differential Algorithm on Hyperspectral Data of Saline Soil

2016 ◽  
Vol 36 (3) ◽  
pp. 0330002 ◽  
Author(s):  
张东 Zhang Dong ◽  
塔西甫拉提·特依拜 Tashpolat·Tiyip ◽  
张飞 Zhang Fei ◽  
阿尔达克·克里木 Ardak·Kelimu ◽  
夏楠 Xia Nan
Keyword(s):  
Saline Soil ◽  
Hyperspectral Data ◽  
Fractional Differential ◽  
Differential Algorithm

scholarly journals Application of Fractional Differential Calculation in Pretreatment of Saline Soil Hyperspectral Reflectance Data

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Anhong Tian ◽  
Junsan Zhao ◽  
Heigang Xiong ◽  
Shu Gan ◽  
Chengbiao Fu
Keyword(s):  
Fractional Order ◽  
Spectral Reflectance ◽  
Model Building ◽  
Saline Soil ◽  
Salt Content ◽  
Soil Salinization ◽  
Human Interference ◽  
Fractional Differential ◽  
Matlab Programming ◽  
Spectrum Data

Pretreatment of spectrum data is a necessary and effective method for improving the accuracy of hyperspectral model building. Traditional differential calculation pretreatment only considers the integer-order differential, such as the 1st order and 2nd order, and overlooks important spectrum information located at fractional order. Since fractional differential (FD) has rarely been applied to spectrum field measurement, there are few reports on the spectrum features of saline soils under different degrees of human interference. We used FD to analyze field spectrum data of saline soil collected from Xinjiang’s Fukang City. Order interval of 0.2 was adopted to divide 0–2 orders into 11-order differentials. MATLAB programming was used to convert the raw spectral reflectance and its four common types of mathematics and to conduct FD calculation. Spectrum data for area A (no human interference area) and area B (human interference area) was separately processed. From the statistical analysis of soil salinization characteristics, the salinization degree and type for area B were more diverse and complicated than area A. MATLAB simulation results showed that FD calculation could depict the minute differences between different FD order spectra under different human interference areas. The overall differential value trend appeared to move towards 0 reflectance value. After differential processing, the trend of bands that passed the 0.05 significance test of correlation coefficient (CC) showed an increase first then decrease later. The maximum CC absolute value for five spectrum transformations all appeared in the fractional order. FD calculation could significantly increase the correlation between spectral reflectance and soil salt content both for full-band and single-band spectra. Results of this study can serve as a reference for the application of FD in field hyperspectral monitoring of soil salinization for different human interference areas.

scholarly journals Land surface temperature vs. Soil spectral reflectance fractional approach and fractional differential algorithm

2019 ◽  
Vol 23 (4) ◽  
pp. 2389-2395
Author(s):  
An-Hong Tian ◽  
Jun-San Zhao ◽  
Zheng-Biao Li ◽  
Hei-Gang Xiong ◽  
Cheng-Biao Fu
Keyword(s):  
Surface Temperature ◽  
Fractional Order ◽  
Land Surface Temperature ◽  
Precision Agriculture ◽  
Land Surface ◽  
Spectral Reflectance ◽  
Variation Characteristics ◽  
Fractional Differential ◽  
Differential Algorithm ◽  
New Perspective

Land surface temperature plays an important role in studying the radiation and energy exchanges between Earth's surface and atmosphere. There is little literature on the relationship between the land surface temperature and the soil spectral reflectance. This paper adopts the Grunwald-Letnikov fractional differential algorithm to reveal their relationship. The simulation results elucidate that a higher land surface temperature will result in a higher spectral reflectance. The variation characteristics of spectral reflectance curves with different land surface temperatures have basically a same trend. Fractional differential order is a good index for spectral change during the derivation process. An optimal fractional order is 6/5, which corresponds to the band of 1710 nm. As the increase of the fractional order, the number of bands increases, but when it reaches a threshold, an opposite trend is found. This study provides a new perspective for adequately excavating spectral data information, and it also can be used as a reference for precision agriculture.

scholarly journals Study on the Pretreatment of Soil Hyperspectral and Na+ Ion Data under Different Degrees of Human Activity Stress by Fractional-Order Derivatives

2021 ◽  
Vol 13 (19) ◽  
pp. 3974
Author(s):  
Anhong Tian ◽  
Junsan Zhao ◽  
Bohui Tang ◽  
Daming Zhu ◽  
Chengbiao Fu ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Fractional Order ◽  
Human Activity ◽  
Saline Soil ◽  
Water Soluble ◽  
Order Derivative ◽  
Continuous Increase ◽  
Integer Order ◽  
Disturbed Area ◽  
Soluble Base

Soluble salts in saline soil often exist in the form of salt base ions, and excessive water-soluble base ions can harm plant growth. As one of the water-soluble base ions, Na+ ion, is the main indicator of the degree of soil salinization. The pretreatment of visible, near infrared and short-wave infrared (VNIR-SWIR) spectroscopy data is the key to establishing a high-precision inversion model, and a proper pretreatment method can fully extract the effective information hidden in the hyperspectral data. Meanwhile, different degrees of human activity stress will have an impact on the ecological environment of oases. However, there are few comparative analyses of the data pretreatment effects for soil water-soluble base ions on the environment under different human interference conditions. Therefore, in this study, the difference in the degree of soil disturbance caused by human activities was used as the basis for dividing the experimental area into lightly disturbed area (Area A), moderately disturbed area (Area B) and severely disturbed zone (Area C). The Grünwald-Letnikov fractional-order derivative (FOD) was used to preprocess the VNIR-SWIR spectroscopic data measured by a FieldSpec®3Hi-Res spectrometer, which could fully extract the useful information hidden in the FOD of the VNIR-SWIR spectroscopy results and avoid the loss of information caused by the traditional integer-order derivative (1.0-order, 2.0-order) pretreatment. The spectrum pretreatment was composed of five transform spectra (R,R, 1/R, lgR, 1/lgR) and 21 FOD methods (step size is 0.1, derivative range is from 0.0- to 2.0-order). In addition, this manuscript compares and analyzes the pretreatment advantages between fractional-order and integer-order. The main results were as follows: (1) Grünwald-Letnikov FOD can reveal the nonlinear characteristics and variation laws of the field hyperspectral of saline soil, namely, due to the continuous performance of the order selection, the FOD accurately depicts the details of spectral changes during the derivation process, and improves the resolution between the peaks of the hyperspectral spectrum. (2) There is a big difference in the shape of the correlation coefficient curve between the original hyperspectral and Na+ at different FOD. The correlation coefficient curve has a clear outline in rang of the 0.0- to 0.6-order, and the change trend is gentle, which presents a certain gradual form. With the continuous increase of the order of the FOD, the change range of the correlation coefficient curve is gradually increased, and the fluctuation is greater between the 1.0-order and the 2.0-order. (3) Regardless of the transformation spectrum and different interference regions, the improvement effect of the FOD on the correlation between hyperspectral and Na+ is significantly better than that of the integer-order derivative. Comparative analysis shows that he percentage of increase of the former is more than 3%, and the highest is more than 17%.

scholarly journals Influence of Fractional Differential on Correlation Coefficient between EC1:5 and Reflectance Spectra of Saline Soil

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Nan Xia ◽  
Tashpolat Tiyip ◽  
Ardak Kelimu ◽  
Ilyas Nurmemet ◽  
Jianli Ding ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Social Economic ◽  
Environmental Issues ◽  
Soil Salinization ◽  
Hyperspectral Data ◽  
Reflectance Spectra ◽  
Ebinur Lake ◽  
Differential Transform ◽  
Ecological Problems ◽  
Fractional Differential

Soil salinization is one of the most serious environmental issues in arid and semiarid area with severe social, economic, and ecological problems. At present, most inversion models are based on raw reflectance spectra or integer differential transform. In this study, we measured the hyperspectral reflectance and EC1:5 of soil samples collected form Ebinur Lake to analyze the influence of fractional differential on correlation coefficient between EC1:5 and reflectance spectra. The results showed that the fractional differential increased sensibly the accuracy for the analysis of the reflectance spectra. The study might provide a new insight for monitoring soil salinity using hyperspectral data, and further researches should be concentrated on physical meaning of fractional differential in hyperspectral data to provide theoretical basis to building, describing, and spreading inversion models.

scholarly journals Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1395
Author(s):  
Charles Castaing ◽  
Christiane Godet-Thobie ◽  
Le Xuan Truong
Keyword(s):  
Fractional Order ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Separable Hilbert Space ◽  
Maximal Monotone ◽  
Fractional Flow ◽  
Order Problem ◽  
Absolutely Continuous ◽  
State Dependent ◽  
Fractional Differential

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.

scholarly journals A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Variable Order ◽  
Fractional Order Systems ◽  
New Approach ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

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