On numerical techniques for solving the fractional logistic differential equation

Abstract

This paper studied the existence and uniqueness of the solution of the fractional logistic differential equation using Hadamard derivative and integral. Previous work has shown that there is not an exact solution to this fractional model. Hence several numerical approaches, such as generalized Euler’s method (GEM), power series expansion (PSE) method, and Caputo–Fabrizio (CF) method, were used to compute the solution. The classical solution obtained from the first order non-linear differential equation was also considered to enable the comparison of error levels.