New numerical method and application to Keller-Segel model with fractional order derivative

Using the fundamental theorem of fractional calculus together with the well-known Lagrange polynomial interpolation, we constructed a new numerical scheme. The new numerical scheme is suggested to solve non-linear and linear partial differential equation with fractional order derivative. The method was used to solve numerically the time fractional Keller-Segel model. The existence and uniqueness solution of the model with fractional Mittag-Leffler kernel derivative are presented in detail. Some simulations are performed to access the efficiency of the newly proposed method.