Mathematical modeling of allelopathic stimulatory phytoplankton species using fractal-fractional derivatives.

In the current study, we employ the novel fractal-fractional operator in the Atangana-Baleanu sense to investigate the dynamics of an interacting phytoplankton species model. Initially, we utilize the Picard-Lindelöf theorem to validate the uniqueness and existence of solutions for the model. We then explore equilibrium points within the phytoplankton model and conduct Hyers-Ulam stability analysis.

A new investigation on fractionalized modeling of human liver.

This study focuses on improving the accuracy of assessing liver damage and early detection for improved treatment strategies. In this study, we examine the human liver using a modified Atangana-Baleanu fractional derivative based on the mathematical model to understand and predict the behavior of the human liver. The iteration method and fixed-point theory are used to investigate the presence of a unique solution in the new model.