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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| Published in | Mathematics (Basel) Vol. 9; no. 19; p. 2370 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
01.10.2021
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| Online Access | Get full text |
| ISSN | 2227-7390 2227-7390 |
| DOI | 10.3390/math9192370 |
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| 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. |
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| AbstractList | 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. |
| Author | Alqahtani, Rubayyi T. Ahmad, Shabir Akgül, Ali |
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| SubjectTerms | 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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| Title | Dynamical Analysis of Bio-Ethanol Production Model under Generalized Nonlocal Operator in Caputo Sense |
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