A computational study of time fractional phytoplankton nutrient model arising in the biological system

Résumé

Microorganisms from the ocean are known as phytoplanktons. We discuss an example of
the nitrogen-limited plankton in the oceans. There are two types of plankton: zooplankton, or
animal plankton, which feeds on phytoplankton, and phytoplankton, or plant plankton, which
photosynthesizes and requires essential nutrients to thrive.Here, we used the Shehu Adomian
decomposition method to and the approximate solutions of time fractional phytoplankton
nutrient model (TFPNM) including fractional order derivatives Caputo, Atangana-Baleanu-
Caputo (ABC), and Caputo-Fabrizio (CF). The biological system emphasises on the dynamics
of phytoplankton-nutrient interaction in the recycling of nutrients. Existence and uniqueness
of TFPNM is provided. Rapidly convergent series solutions are provided by the proposed tech-
nique. A comparison of the Caputo, ABC, and CF derivatives are included. A thorough study
has been done on the graphical representation of the impact of arbitrary order derivatives.