Hattaf fractional derivative

Catalytic action is one of the most important characteristics of enzymes in chemical reactions.  In this article, we propose and study a mathematical model of chemical kinetic reaction with the memory effect using the new generalized Hattaf fractional derivative.  The existence and uniqueness of the solutions are established by means of fixed point theory and, finally, to support the theoretical results, we end the article with the results of numerical simulations based on a novel numerical scheme that includes the Euler method.

In this paper, we propose and analyze a fractional prey–predator  model with generalized Hattaf fractional (GHF) derivative.  We prove that our proposed model is ecologically and mathematically well-posed.  Furthermore, we show that our model has three equilibrium points.  Finally, we establish the stability of these equilibria.