Fractal fractional derivative on chemistry kinetics hires problem

Muhammad Aslam; Muhammad Farman; Hijaz Ahmad; Tuan Nguyen Gia; Aqeel Ahmad; Sameh Askar; Muhammad Aslam; Muhammad Farman; Hijaz Ahmad; Tuan Nguyen Gia; Aqeel Ahmad; Sameh Askar

doi:10.3934/math.2022068

AIMS Mathematics

2022, Volume 7, Issue 1: 1155-1184. doi: 10.3934/math.2022068

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Research article

Fractal fractional derivative on chemistry kinetics hires problem

1.
Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of Ministry of Education, Department of Chemistry and Materials Science, Northwest University, Xi'an 710127, China
2.
Department of Mathematics and Statistics, University of Lahore, Lahore 54590, Pakistan
3.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy
4.
Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq
5.
Department of Computing, University of Turku, 20500, Turku, Finland
6.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 28 July 2021 Accepted: 21 September 2021 Published: 21 October 2021
MSC : 37C75, 93B05, 65L07

In this work, we construct the fractional order model for chemical kinetics issues utilizing novel fractal operators such as fractal fractional by using generalized Mittag-Leffler Kernel. To overcome the constraints of the traditional Riemann-Liouville and Caputo fractional derivatives, a novel notion of fractional differentiation with non-local and non-singular kernels was recently presented. Many scientific conclusions are presented in the study, and these results are supported by effective numerical results. These findings are critical for solving the nonlinear models in chemical kinetics. These concepts are very important to use for real life problems like brine tank cascade, recycled brine tank cascade, pond pollution, home heating and biomass transfer problem. Many scientific results are presented in the paper also prove these results by effective numerical results. These results are very important for solving the nonlinear model in chemistry kinetics which will be helpful to understand the chemical reactions and its actual behavior; also the observation can be developed for future kinematic chemical reactions with the help of these results.
- chemistry kinetics,
- fractal fractional derivative,
- Mittag-Leffler kernel,
- stability,
- Uniqueness
Citation: Muhammad Aslam, Muhammad Farman, Hijaz Ahmad, Tuan Nguyen Gia, Aqeel Ahmad, Sameh Askar. Fractal fractional derivative on chemistry kinetics hires problem[J]. AIMS Mathematics, 2022, 7(1): 1155-1184. doi: 10.3934/math.2022068

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Abstract

In this work, we construct the fractional order model for chemical kinetics issues utilizing novel fractal operators such as fractal fractional by using generalized Mittag-Leffler Kernel. To overcome the constraints of the traditional Riemann-Liouville and Caputo fractional derivatives, a novel notion of fractional differentiation with non-local and non-singular kernels was recently presented. Many scientific conclusions are presented in the study, and these results are supported by effective numerical results. These findings are critical for solving the nonlinear models in chemical kinetics. These concepts are very important to use for real life problems like brine tank cascade, recycled brine tank cascade, pond pollution, home heating and biomass transfer problem. Many scientific results are presented in the paper also prove these results by effective numerical results. These results are very important for solving the nonlinear model in chemistry kinetics which will be helpful to understand the chemical reactions and its actual behavior; also the observation can be developed for future kinematic chemical reactions with the help of these results.

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