Analytical Approximate Solution of the Fractional Order Biological Population Model by Using Natural Transform

Abstract

In the present work, the natural transform iterative method (NTIM) is implemented to solve the biological population model (BPM) of fractional order. The method is tested for three nonlinear examples. The NTIM is a combination of a new iterative method and natural transform. We see that the solution pattern converges to the exact solution in a few iterations. The method handles an extensive range of differential equations of both fractional and integer order. The fractional order derivative is considered in Caputo’s sense. For mathematical computation, Mathematica 10 is used.

Studying of COVID-19 fractional model: Stability analysis

“…In other words, the description of epidemic models by using fractional differential equations takes into account all historical and current states, which makes them more realistic and more general in nature. 37 , 38 This prompted us to develop the Caputo fractional mathematical model for COVID-19 and introduce details about the existence of a unique positive solution and its behaviour. In spite of the fact that there are many definitions of a fractional derivative, many scholars prefer to use the Caputo derivative to describe mathematical models by means of FDEs.…”