Numerical Solution of Fractional Logistic Differential Equation via LRPSM

The Laplace transform with residual power series method (LRPSM) is one of the efficient and reliable methods for solution of fractional order linear and non-linear differential equations. The aim of this work is to find the solution of fractional order non-linear logistic differential equation by using LRPSM. The Caputo fractional operator is used to define the fractional order derivative. The fractional derivative in this case is described by Caputo. We pay particular attention to the stability, existence, and uniqueness of the fractional-order logistic equation. This equation's exact and approximate solutions are compared via LRPSM, and the results are computed and displayed in a graph. Similar to the conventional RPS method, the unknown coefficients of the succession are determined. This method reduces the size of computational works and the solution is obtained in series form.