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

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.