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Dynamical Analysis of Bio-Ethanol Production Model under Generalized Nonlocal Operator in Caputo Sense

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  • Rubayyi T. Alqahtani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

  • Shabir Ahmad

    (Department of Mathematics, University of Malakand, Dir Lower 18300, Khyber Pakhtunkhwa, Pakistan)

  • Ali Akgül

    (Department of Mathematics, Art and Science Faculty, Siirt University, Siirt TR-56100, Turkey)

Abstract

The nonlinear fractional-order model of bioethanol production under a generalized nonlocal operator in the Caputo sense is investigated in this work. Theoretical and computational aspects of the considered model are discussed. We prove that the model has at least one solution and a unique solution using the Leray–Schauder and Banach contraction theorems. Using functional analysis, we investigate several types of Ulam–Hyres model stability. We use the predictor–corrector (P–C) method to construct a broad numerical scheme for the model’s solution. The proposed numerical method’s stability is demonstrated. Finally, we depict the numerical findings geometrically to demonstrate the model’s dynamics.

Suggested Citation

  • Rubayyi T. Alqahtani & Shabir Ahmad & Ali Akgül, 2021. "Dynamical Analysis of Bio-Ethanol Production Model under Generalized Nonlocal Operator in Caputo Sense," Mathematics, MDPI, vol. 9(19), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2370-:d:642224
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    References listed on IDEAS

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    1. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 111-119.
    2. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    Cited by:

    1. Mahmood, Tariq & Al-Duais, Fuad S. & Sun, Mei, 2022. "Dynamics of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) involving fractional derivative with Mittag-Leffler kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    2. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Saifullah, Sayed & Inc, Mustafa, 2022. "Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana–Baleanu fractional operator: Real data approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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