Title: Water Engineering Modeling Controlled by Generalized Tsallis Entropy
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-20-00040; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 227-237
Document Type: Research Paper
aIEEE: 94086547, Kuala Lumpur, 59200, Malaysia
Received: 10 November 2020, Accepted: 10 March 2021, Published: 25 April 2021.
Corresponding Author: Rabha Waell Ibrahim (Email address: email@example.com)
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Water engineering is a real live, study that combines engineering and non-engineering factors that are realized for operating water schemes. These facets and the connected problems applying various procedures. We formulate a new type of the chi-square distributions, which is given in terms of the local fractional integral (fractal integral operator). This concept is a special part of fractional calculus. Then the fractal chi-square will employ to generalize Tsallis entropy. These types of entropy have been seen in numerous applications in almost all the sciences, including the social sciences and humanities studies. We scheme a unique form of the fractal Tsallis entropy using fractal chi-square test. A test method is talented of studying water engineering modeling.
Keywords: Chi-square, Fractional calculus, Fractal, Laplace transform, Wave modeling, Fractional differential equation, Fractional operatorReferences:
- M. Kazolea and M. Ricchiuto, On wave breaking for Boussinesq-type models, Ocean Modelling 123, 16-39, 2018.
- R. W. Ibrahim, C. Meshram, S. B. Hadid and S. Momani, Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator, Journal of Ocean Engineering and Science 5 (2), 186-195, 2020.
- V. P. Singh, B. Sivakumar and H. Cui, Tsallis entropy theory for modeling in water engineering: A review, Entropy 19 (12), 641, 2017.
- V. P. Singh, Entropy Theory in Hydrologic Science and Engineering, McGraw-Hill Education, New York, NY, USA, 2015.
- C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1-2), 479-487, 1988.
- C. Tsallis and U. Tirnakli, Predicting COVID-19 peaks around the world, Front. Phys. 8, 217, 2020.
- M. Shaher, R. W. Ibrahim and S. B. Hadid, Susceptible-infected-susceptible epidemic discrete dynamic system based on Tsallis entropy, Entropy 22 (7), 1-11, 2020.
- R. W. Ibrahim, Utility function for intelligent access web selection using the normalized fuzzy fractional entropy, Soft Comput. 1-8, 2020.
- R. W. Ibrahim, H. Jafari, H. A. Jalab and S. B. Hadid, Local fractional system for economic order quantity using entropy solution, Adv. Difference Equ. 2019 (1), 1-11, 2019.
- R. W. Ibrahim, The fractional differential polynomial neural network for approximation of functions, Entropy 15, 4188-4198, 2013.
- R. W. Ibrahim and H. A. Jalab, Existence of Ulam stability for iterative fractional differential equations based on fractional entropy, Entropy 17 (5), 3172-3181, 2015.
- R. W. Ibrahim and M. Darus, Analytic study of complex fractional Tsallis’ entropy with applications in CNNs, Entropy 20 (10), 1-11, 2018.
- H. Jalab, R. W. Ibrahim and A. Ahmed, Image denoising algorithm based on the convolution of fractional Tsallis entropy with the Riesz fractional derivative, Neural Comput. Appl. 28 (1), 217-223, 2017.
- R. W. Ibrahim, A. H. Jalab and A. Gani, Perturbation of fractional multi-agent systems in cloud entropy computing, Entropy 18 (1), 1-13, 2016.
- T. M. Semkow, et.al., Chi-square distribution: New derivations and environmental application, Journal of Applied Mathematics and Physics 7 (8), 1786, 2019.
- H. O. Lancaster, The Chi-Squared Distribution, J. Wiley & Sons, New York, Chap. 1, 1969.
- P. Gorroochurn, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times, J. Wiley & Sons, Hoboken, Chap. 3, 2016.
- A. Stuart and K. Ord, Kendall’s Advanced Theory of Statistics, Distribution Theory, Vol. 1, Arnold Hodder Headline Group, London, Chap. 11, 1994.
- S. Ross, A First Course in Probability, Pearson Prentice Hall, Upper Saddle, River, Sec. 6 (3), 2006.
- X-J. Yang, D. Baleanu and H. M. Srivastava, Local Fractional Integral Transforms and Their Applications, Academic Press, 2015.