ON SOLUTIONS OF INITIAL VALUE PROBLEM FOR NONLINEAR FRACTIONAL BERNOULLI EQUATIONS

Abstract

Abstract:

This research article discusses the Adomian decomposition method that has been applied to solving second-order the nonlinear (linear) fractional differential equation for the Bernoulli equation with initial conditions. Firstly, the Bernoulli equation with fractional derivatives is transferred to a nonlinear (linear) fractional differential equation subject to initial conditions. Then it investigated the existence of approximate solutions to this type of initial value problem by applying Adomian decomposition technique. In view of the convergence of this method, some illustrative examples are included to demonstrate the proposed technique and show the efficiency of the presented method.
Keywords: Fractional differential equation; Adomian decomposition method; Caputo fractional derivative; the Bernoulli differential equation with fractional derivative.