THE GENERALIZED TIME FRACTIONAL GARDNER EQUATION VIA NUMERICAL MESHLESS COLLOCATION METHOD - Mehnaz, Shakeel; Khan, Muhammad Nawas; Ahmad, Imtiaz; Abdel-Khalek, Sayed; Alghamdi, Ahmed Mohammed; İnç, Mustafa (Vinca Inst Nuclear Sci, 2022)
In this study, the meshless collocation approach is used to determine the numerical solution the generalized time-fractional Gardner equation. The Crank-Nicolson technique is used to approximate space derivatives, whereas the Caputo derivative of fractional order is used to approximate the first order time fractional derivative. The numerical solutions, which show the method's efficacy and accuracy, are provided and discussed. The numerical solution shows that our method is effective in producing extremely accurate results.
Keywords: time-fractional Gardner equation; Crank-Nicolson scheme; radial basis functions; Caputo fractional derivative