Estimating Approximate Solutions of Non-Linear Caputo Fractional Differential Equations with Forcing Functions Using Picard's Iteration Method

Abstract

The objective of this research is to extend the applicability of Picard's iterative existence and uniqueness theorem in solving non-linear Caputo fractional differential equations of higher order that involve a forcing function satisfying the usual Lipchitz's condition. To demonstrate the effectiveness of our approach, we have presented numerical examples of order α (where 1 < α < 2 and 2 < α < 3) along with the application of the fractional damped duffing oscillator. The solutions obtained through Picard's iterative method are accompanied by graphical representations and some solutions compared with ADM solutions using graphs.