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Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel

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  • Qureshi, Sania
  • Aziz, Shaheen

Abstract

Various physical systems exhibit non-Markovian (hereditary and memory effects) characteristics in their very inherent structures. In this research study, the fractional (non-classical) differential operator of Caputo’s type is used to analyze such a physical system representing chemical kinetic reactions in a batch reactor. The governing system of fractional order equations under Caputo’s type derivative is formulated and later solved via Laplace integral transform and its inversion. Analytically obtained general solutions of the governing equations are expressed in the form of special Mittag-Leffler function and power series expansion with double summation. During fractionalization, the dimensional analysis has been taken care of and the results are graphically illustrated. The obtained simulation results for varying values of fractional-order α represented various behavior with the fractional Caputo’s type governing equations for the concentration of three species. In other words, varying memory effects are observed during simulations of the model based upon different values of α and the rate constants. The classical model is retrieved for the limiting case when α→1.

Suggested Citation

  • Qureshi, Sania & Aziz, Shaheen, 2020. "Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    • Handle: RePEc:eee:phsmap:v:542:y:2020:i:c:s0378437119319508
    DOI: 10.1016/j.physa.2019.123494
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    References listed on IDEAS

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    1. Abu Arqub, Omar & Maayah, Banan, 2019. "Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 163-170.
    2. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    3. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
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    5. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    6. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    7. Aliyu, Aliyu Isa & Inc, Mustafa & Yusuf, Abdullahi & Baleanu, Dumitru, 2018. "A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 268-277.
    8. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    9. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    10. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
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    2. J., Kokila & M., Vellappandi & D., Meghana & V., Govindaraj, 2023. "Optimal control study on Michaelis–Menten kinetics — A fractional version," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 571-592.

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