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

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 u...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 19; p. 2370
Main Authors Alqahtani, Rubayyi T., Ahmad, Shabir, Akgül, Ali
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2021
Subjects
Applied mathematics
Biofuels
Biomass
Ethanol
ethanol model
Food science
Functional analysis
generalized Caputo derivative
Growth rate
Mathematical models
Numerical methods
Stability analysis
Ulam-Hyres-Rassias stable
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ISSN2227-7390
2227-7390
DOI10.3390/math9192370

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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9192370