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.
Highlights
Introduction and MotivationScientists and industry have been focusing on the creation of green, sustainable biorefineries in recent years
We investigated a fractional mathematical model for the synthesis of bio-ethanol using a generalised Caputo operator
We have established the algorithm via a numerical method called the predictor–corrector method to find the approximate solution of the dimensionless ethanol model
Summary
Scientists and industry have been focusing on the creation of green, sustainable biorefineries in recent years. The third equation of the model represents the rate of change of the ethanol It depends on the use of a settling unit and a flow-through reactor. The numerical solution of the initial value problem with the Caputo fractional differential equation has been introduced in [19] using an Adams-type P–C technique In the literature, this approach has been widely utilized to simulate several fractional derivative models, including the work reported in [29,30,31,32]. This derivative has recently introduced and its applications in modelling of any physical phenomena are very rare We use this newly developed generalized Caputo derivative to study the bioethanol model. The numerical results are graphically presented to study the process of the ethanol production and effects of the generalized Caputo operator on the evolution of the proposed ethanol model
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
