Abstract
The principal aim of the present article is to study a mathematical pattern of interacting phytoplankton species. The considered model involves a fractional derivative which enjoys a nonlocal and nonsingular kernel. We first show that the problem has a solution, then the proof of the uniqueness is included by means of the fixed point theory. The numerical solution of the mathematical model is also obtained by employing an efficient numerical scheme. From numerical simulations, one can see that this is a very efficient method and provides precise and outstanding results.