Study of Variable Order Mathematical Model by Using Algae as Bio-Fertilizers

Shah K., Abdeljawad T., Aiady S. S., Arfan M.

Journal of Nonlinear Mathematical Physics, vol.32, no.1, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1007/s44198-025-00331-3
  • Journal Name: Journal of Nonlinear Mathematical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Model of agriculture, Qualitative analysis, Variable order Adams-Bashforth technique, Variable order derivative
  • Istanbul Gelisim University Affiliated: No

Abstract

A bio-fertilization mathematical model of algae population under variable order derivative (VOD) is considered. Some appropriate results are derived for the existence, stability and numerical analysis. The existence and unique results are derived for the proposed system with the help of the fixed point analysis. Further, for the local stability of the model, we use Ulam-Hyers (U-H) concept. The approximation for each quantity is calculated by the method of variable order Adams Bashforth predictor corrector method. Various graphical representations of different compartments are shown by using different values of variable orders. Several graphical representations are displayed to verify the sensitivity of different parameters at different variable orders of the proposed model.