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 Classifying and Predicting Salinization Level in Arid Area Soil Using a Combination of Chua’s Circuit and Fractional Order Sprott Chaotic System

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4517 ◽  
Author(s):  
Tian ◽  
Fu ◽  
Su ◽  
Yau ◽  
Xiong
Keyword(s):  
Chemical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Element Model ◽  
Soil Salinization ◽  
Arid Area ◽  
Classification Model ◽  
Human Interference ◽  
Matter Element Model ◽  
Different Levels

Soil salinization is very complex and its evolution is affected by numerous interacting factors produce strong non-linear characteristics. This is the first time fractional order chaos theory has been applied to soil salinization-level classification to decrease uncertainty in salinization assessment, solve fuzzy problems, and analyze the spectrum chaotic features in soil with different levels of salinization. In this study, typical saline soil spectrum data from different human interference areas in Fukang City (Xinjiang) and salt index test data from an indoor chemical analysis laboratory are used as the base information source. First, we explored the correlation between the spectrum reflectance features of soil with different levels of salinization and chaotic dynamic error and chaotic attractor. We discovered that the chaotic status error in the 0.6 order has the greatest change. The 0.6 order chaotic attractors are used to establish the extension matter-element model. The determination equation is built according to the correspondence between section domain and classic domain range to salinization level. Finally, the salt content from the chemical analysis is substituted into the discriminant equation in the extension matter-element model. Analysis found that the accuracy of the discriminant equation is higher. For areas with no human interference, the extension classification can successfully identify nine out of 10 prediction data, which is a 90% identification accuracy rate. For areas with human interference, the extension classification can successfully identify 10 out of 10 prediction data, which is a success rate of 100%. The innovation in this study is the building of a smart classification model that uses a fractional order chaotic system to inversely calculate soil salinization level. This model can accurately classify salinization level and its predictive results can be used to rapidly calculate the temporal and spatial distribution of salinization in arid area/desert soil.

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.

scholarly journals Hyperspectral Prediction of Soil Total Salt Content by Different Disturbance Degree under a Fractional-Order Differential Model with Differing Spectral Transformations

2021 ◽  
Vol 13 (21) ◽  
pp. 4283
Author(s):  
Anhong Tian ◽  
Junsan Zhao ◽  
Bohui Tang ◽  
Daming Zhu ◽  
Chengbiao Fu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Salt Content ◽  
Soil Salinization ◽  
The Other ◽  
Optimal Model ◽  
Differential Model ◽  
Significance Level ◽  
Disturbed Area ◽  
Total Salt Content ◽  
Plsr Model

Soil salinization is an ecological challenge across the world. Particularly in arid and semi-arid regions where evaporation is rapid and rainfall is scarce, both primary soil salinization and secondary salinization due to human activity pose serious concerns. Soil is subject to various human disturbances in Xinjiang in this area. Samples with a depth of 0–10 cm from 90 soils were taken from three areas: a slightly disturbed area (Area A), a moderately disturbed area (Area B), and a severely disturbed area (Area C). In this study, we first calculated the hyperspectral reflectance of five spectra (R, R, 1/R, lgR, 1/lgR, or original, root mean square, reciprocal, logarithm, and reciprocal logarithm, respectively) using different fractional-order differential (FOD) models, then extracted the bands that passed the 0.01 significance level between spectra and total salt content, and finally proposed a partial least squares regression (PLSR) model based on the FOD of the significance level band (SLB). This proposed model (FOD-SLB-PLSR) is compared with the other three PLSR models to predict with precision the total salt content. The other three models are All-PLSR, FOD-All-PLSR, and IOD-SLB-PLSR, which respectively represent PLSR models based on all bands, all fractional-order differential bands, and significance level bands of the integral differential. The simulations show that: (1) The optimal model for predicting total salt content in Area A was the FOD-SLB-PLSR based on a 1.6 order 1/lgR, which provided good predictability of total salt content with a RPD (ratio of the performance to deviation) between 1.8 and 2.0. The optimal model for predicting total salt content in Area B was a FOD-SLB-PLSR based on a 1.7 order 1/R, which showed good predictability for total salt content with RPDs between 2.0 and 2.5. The optimal model for predicting total salt content in Area C was a FOD-SLB-PLSR based on a 1.8 order lgR, which also showed good predictability for total salt content with RPDs between 2.0 and 2.5. (2) Soils subject to various disturbance levels had optimal FOD-SLB-PLSR models located in the higher fractional order between 1.6 and 1.8. This indicates that higher-order FODs have a stronger ability to extract feature data from complex information. (3) The optimal FOD-SLB-PLSR model for each area was superior to the corresponding All-PSLR, FOD-All-PLSR, and IOD-SLB-PLSR models in predicting total salt content. The RPD value for the optimal FOD-SLB-PLSR model in each area compared to the best integral differential model showed an improvement of 9%, 45%, and 22% for Areas A, B, and C, respectively. It further showed that the fractional-order differential model provides superior prediction over the integral differential. (4) The RPD values that provided an optimal FOD-SLB-PLSR model for each area were: Area A (1.9061) < Area B (2.0761) < Area C (2.2892). This indicates that the prediction effect of data processed by fractional-order differential increases with human disturbance increases and results in a higher-precision model.

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 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 Bioremediation of polluted soil due to tsunami by using recycled waste glass

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Azizul Moqsud
Keyword(s):  
Heavy Metals ◽  
Electrical Conductivity ◽  
Laboratory Experiments ◽  
Saline Soil ◽  
Salt Content ◽  
Tohoku Earthquake ◽  
Polluted Soil ◽  
Waste Glass ◽  
Excess Cost ◽  
Recycled Waste

AbstractIn this research, bioremediation of tsunami-affected polluted soil has been conducted by using collective microorganisms and recycled waste glass. The Tohoku earthquake, which was a mega earthquake in Japan triggered a huge tsunami on March 11th, 2011 that caused immeasurable damage to the geo-environmental conditions by polluting the soil with heavy metals and excessive salt content. Traditional methods to clean this polluted soil was not possible due to the excess cost and efforts. Laboratory experiments were conducted to examine the capability of bioremediation of saline soil by using recycled waste glass. Different collective microorganisms which were incubated inside the laboratory were used. The electrical conductivity (EC) was measured at different specified depths. It was noticed that the electrical conductivity decreased with the assist of the microbial metabolisms significantly. Collective microorganisms (CM2) were the highly capable to reduce salinity (up to 75%) while using recycled waste glass as their habitat.

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.

Sign in / Sign up

Export Citation Format

Share Document