A NUMERICAL STUDY OF COMPLEX DYNAMICS OF A CHEMOSTAT MODEL UNDER FRACTAL-FRACTIONAL DERIVATIVE

Zareen A. Khan, Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

In this paper, we study the existence of numerical solution and stability of a chemostat model under fractal-fractional order derivative. First, we investigate the positivity and roundedness of the solution of the considered system. Second, we find the existence of a solution of the considered system by employing the Banach and Schauder fixed-point theorems. Furthermore, we obtain a sufficient condition that allows the existence of the stabling of solutions by using the numerical-functional analysis. We find that the proposed system exists as a unique positive solution that obeys the criteria of Ulam–Hyers (U-H) and generalized U-H stability. We also establish a numerical analysis for the proposed system by using a numerical scheme based on the Lagrange interpolation procedure. Finally, we provide two numerical examples to verify the correctness of the theoretical results. We remark that the structure described by the considered model is also sometimes called side capacity or cross-flow model. The structure considered here can be also seen as a limiting case of the pattern chemostats in parallel with diffusion connection. Moreover, the said model forms in natural and engineered systems and can significantly affect the hydrodynamics in porous media. Fractal calculus is an excellent tool to discuss fractal characteristics of porous media and the characteristic method of the porous media.

Original languageEnglish
Article numbere2340181
JournalFractals
Volume31
Issue number8
DOIs
Publication statusPublished - 2023
Externally publishedYes

Keywords

  • Chemostat Model
  • Fixed-point Theorem
  • Fractal-fractional Order Derivative
  • Numerical Solution
  • Stability

Fingerprint

Dive into the research topics of 'A NUMERICAL STUDY OF COMPLEX DYNAMICS OF A CHEMOSTAT MODEL UNDER FRACTAL-FRACTIONAL DERIVATIVE'. Together they form a unique fingerprint.

Cite this