an approximation technique for a system of time-fractional differential equations arising in population dynamics

In this work, we develop and analyze an approximation technique for the system of time-fractional nonlinear differential equations arising in population dynamics. the fractional of order $ sigmain(0,1) $ is taken in the caputo sense. the proposed technique uses l1 discretization on the uniform mesh to approximate the differential operator. the fractional model is transformed into a system of nonlinear algebraic equations. the generalized newton-raphson method is employed to solve the corresponding nonlinear system. a rigorous error estimation is presented. it is shown that the proposed scheme achieved $ (2-sigma) $ order of accuracy. lastly, numerical experiment is conducted to demonstrate the validity of the proposed technique.