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[Vol. 07, No. 06] [June 2021]
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| Paper Title | :: | Fractional Taylor Series Based on Jumarie Type of Modified Riemann-Liouville Derivatives |
| Author Name | :: | Chii-Huei Yu |
| Country | :: | China |
| Page Number | :: | 01-06 |
In this paper, based on the Jumarie type of modified Riemann-Liouville (R-L) fractional derivatives, we use a new multiplication, fractional Taylor series method and chain rule for fractional derivatives to find the fractional Taylor series expansions of some fractional functions.These results we obtained are the generalizations of Taylor series expansions of several classical functions.
Key Words: Jumarie type of R-L derivatives,new multiplication,fractional Taylor series, chain rule
Key Words: Jumarie type of R-L derivatives,new multiplication,fractional Taylor series, chain rule
[1]. F. Mainardi, Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models, World Scientific, 2010.
[2]. R. L. Magin, Fractional calculus in bioengineering, 13th International Carpathian Control Conference, 2012.
[3]. G. M., Zaslavsky, Hamiltonian chaos and fractional dynamics, Oxford University Press, Oxford, 2005.
[4]. A. Carpinteri, F. Mainardi, (Eds.), Fractals and fractional calculus in continuum mechanics, Springer, Wien, 1997.
[5]. Mohd. Farman Ali, Manoj Sharma, Renu Jain, An application of fractional calculus in electrical engineering, Advanced Engineering Technology and Application, 5(2), 2016, 41-45.
[2]. R. L. Magin, Fractional calculus in bioengineering, 13th International Carpathian Control Conference, 2012.
[3]. G. M., Zaslavsky, Hamiltonian chaos and fractional dynamics, Oxford University Press, Oxford, 2005.
[4]. A. Carpinteri, F. Mainardi, (Eds.), Fractals and fractional calculus in continuum mechanics, Springer, Wien, 1997.
[5]. Mohd. Farman Ali, Manoj Sharma, Renu Jain, An application of fractional calculus in electrical engineering, Advanced Engineering Technology and Application, 5(2), 2016, 41-45.
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- Abstract
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| Paper Title | :: | Analysis of Sulfur Dioxide Concentrations in México City, trend 2010 - 2020 |
| Author Name | :: | M. Sc. Zenteno Jiménez José Roberto |
| Country | :: | Mexico |
| Page Number | :: | 07-15 |
The study comprises an analysis of data from 2010 to 2020, it was proposed to obtain the best or best probability distribution functions that model SO2 concentrations in México City, using the following pdf, T location scale distribution function, extreme value distribution function and exponential distribution function, to obtain the estimators the method of maximum likelihood and moments was used and aided by the Matlab program, for valuation of the forecast model, RMSE, MSE, coefficient of determination, approximation of prediction and approximation index, in turn an analysis is made to observe its trend with an analysis of variance, the daily concentration data is downloaded from the official monitoring page and corroborating with the official air page of México City.
Key Words: Sulfur Dioxide, Probability Distributions, Adjustment Indicators, Analysis of Variance.
Key Words: Sulfur Dioxide, Probability Distributions, Adjustment Indicators, Analysis of Variance.
[1]. A.J. Jakeman, J.A. Taylor, R.W. Simpson, Modeling distributions of air pollutant concentrations - II. Estimation of one and two parameters statistical distributions, Atmos. Environ., 20 (1986) 2435-2447.
[2]. Berger, A., Melice, J. L. and Demuth, C. L. (1982) Statistical distributions of daily and high atmospheric SO2 – concentrations. Atmospheric Environment. 16 (5), 2863 – 2877
[3]. Data base of PM2.5 website of México City http://www.aire.cdmx.gob.mx/
[4]. Georgopoulos, P.G. and Seinfeld, J.H. (1982) ‘Statistical distribution of air pollutant concentration’, Environmental Science Technology, Vol. 16, pp.401A–416A.
[5]. Gumbel, E.J., 1958. Statistics of Extremes. Columbia University Press, New York, p. 164.
[2]. Berger, A., Melice, J. L. and Demuth, C. L. (1982) Statistical distributions of daily and high atmospheric SO2 – concentrations. Atmospheric Environment. 16 (5), 2863 – 2877
[3]. Data base of PM2.5 website of México City http://www.aire.cdmx.gob.mx/
[4]. Georgopoulos, P.G. and Seinfeld, J.H. (1982) ‘Statistical distribution of air pollutant concentration’, Environmental Science Technology, Vol. 16, pp.401A–416A.
[5]. Gumbel, E.J., 1958. Statistics of Extremes. Columbia University Press, New York, p. 164.