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

Rubayyi T. Alqahtani, Shabir Ahmad and Ali Akgül
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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

Mathematics, 2021, vol. 9, issue 19, 1-21

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.

Keywords: ethanol model; Ulam-Hyres-Rassias stable; generalized Caputo derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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