Caputo Fractal Fractional Order Derivative of Soil Pollution Model Due to Industrial and Agrochemical

This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard conditi...

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Vydáno v:International journal of applied and computational mathematics Ročník 8; číslo 5; s. 250
Hlavní autoři: Priya, P., Sabarmathi, A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New Delhi Springer India 01.01.2022
Springer Nature B.V
Témata:
Agrochemicals
Algorithms
Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Exact solutions
Fixed points (mathematics)
Fractal models
Fractional calculus
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Operators (mathematics)
Original Paper
Perturbation
Qualitative analysis
Soil analysis
Soil pollution
Stability analysis
Theoretical
Ulam Hyer stability
Agrochemical
Power law kernel
Fractal dimension
Euler method
ISSN:2349-5103, 2199-5796, 2199-5796
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Abstract This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder’s fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders ( 0.5 < η < 1 ) and validating the theoretical parameter values of real time data by the support of MATLAB.
AbstractList This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder's fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders ( 0.5 < η < 1 ) and validating the theoretical parameter values of real time data by the support of MATLAB.This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder's fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders ( 0.5 < η < 1 ) and validating the theoretical parameter values of real time data by the support of MATLAB.
This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder's fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders and validating the theoretical parameter values of real time data by the support of MATLAB.
This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder’s fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders (0.5<η<1) and validating the theoretical parameter values of real time data by the support of MATLAB.
This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder’s fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders $$(0.5<\eta <1)$$ (0.5<η<1) and validating the theoretical parameter values of real time data by the support of MATLAB.
This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder’s fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders ( 0.5 < η < 1 ) and validating the theoretical parameter values of real time data by the support of MATLAB.
ArticleNumber 250
Author Priya, P.
Sabarmathi, A.
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Issue 5
Keywords Ulam Hyer stability
Agrochemical
Power law kernel
Fractal dimension
Euler method
Language English
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Snippet This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five...
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SubjectTerms Agrochemicals
Algorithms
Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Exact solutions
Fixed points (mathematics)
Fractal models
Fractional calculus
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Operators (mathematics)
Original Paper
Perturbation
Qualitative analysis
Soil analysis
Soil pollution
Stability analysis
Theoretical
Title Caputo Fractal Fractional Order Derivative of Soil Pollution Model Due to Industrial and Agrochemical
URI https://link.springer.com/article/10.1007/s40819-022-01431-0
https://www.ncbi.nlm.nih.gov/pubmed/36091873
https://www.proquest.com/docview/2709943915
https://www.proquest.com/docview/2713307392
https://pubmed.ncbi.nlm.nih.gov/PMC9443653
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