Numerical Solutions of Certain New Models of the Time-Fractional Gray-Scott

A reaction-diffusion system can be represented by the Gray-Scott model. In this study, we discuss a one-dimensional time-fractional model with Liouville-Caputo, Caputo-Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional derivatives. We utilize homotopy analysis transformation method to obtain approximate solutions for This gives more realistic series of that converge rapidly exact solution. ensure convergence solving resultant. study determining interval employing ℏ u , v -curves average residual error. also test accuracy efficiency comparing our results numerically Moreover, effect fractionally obtained derivatives on is analyzed. The algorithm easily applied singular nonsingular derivative partial differential equations, where few terms solution are good enough give an accurate