BERNOULLI DIFFERENTIAL EQUATION OF SECOND ORDER WITH FRACTIONAL DERIVATIVE

Abstract

In this study, we present a second order nonlinear equation with nonlinearity of Bernoulli type, which include fractional order derivatives. We consider the numerical solution of the nonlinear equation using the Picard iteration method, the method seeks to examine the convergence of solutions of this type of equations. The resulting solution showed that the convergence could be increased at each iterate level. However, as the number of iterations increases, there is a rapid rate of convergence of the approximate solution to the analytic solution. All Results obtained with the classical Picard method on the equation and were compared with the exact solution.