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Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order

Chinese Physics B 2017年第4期26卷 66-74页

作者：何秋燕余波袁晓 College of Electronics and Information Engineering Sichuan University College of Physics and Engineering Chengdu Normal University

The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this *** reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained.K-index,P-index,O-index,and complexity index are introduced to contribute to performance *** nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order,these rational approximation impedance functions calculated by the iterating function meet computational rationality,positive reality,and operational *** they are capable of having the operational performance of fractional operators and being physical *** approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.

关键词： fractional calculus fractional operator generalized Carlson iterating process approximation error

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Modeling Dysentery Diarrhea Using Statistical Period Prevalence

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Computer Modeling in Engineering & Sciences 2021年第7期128卷 183-201页

作者： Fouad A.Abolaban Department of Nuclear Engineering College of EngineeringKing Abdulaziz UniversityJeddah21589Saudi Arabia

Various epidemics have occurred throughout history,which has led to the investigation and understanding of their transmission *** a result,non-local operators are used for mathematical modeling in this ***,this research focuses on developing a dysentery diarrhea model with the use of a fractional operator using a one-parameter Mittag–Leffler *** model consists of three classes of the human population,whereas the fourth one belongs to the pathogen *** model carefully deals with the dimensional homogeneity among the parameters and the fractional *** addition,the model was validated by fitting the actual number of dysentery diarrhea infected cases covering 52 weeks in 2017,which occurred in *** biological parameters were fitted,and fractional orderνwas *** basic reproduction numbers R0 were 1.7031 and 1.9581,which correspond to the fractional and integer-order models,*** fractional model showed smaller discrepancies compared to the integer-order model when the models were fitted and validated with the actual cases of infected *** theory for the existence and uniqueness of the solutions was extensively explored,and the stability of equilibria was *** most influential parameters were found via forward sensitivity *** multidisciplinary research shows and explains the results of numerical simulations applied to a biological issue.

关键词： Dysentery diarrhea model Mittag–Leffler kernel fractional operator

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