An Analytical Approach to Nonlinear Fractional Differential Equations Using Daftardar-Jafari Method

Fractional differential equations have gained significant attention in recent years due to their ability to model complex phenomena in various scientific and engineering fields. This study focuses on solving fractional differential equations involving the nonlinear Caputo fractional derivative and the Caputo-Fabrizio fractional derivative. We employ the Daftardar-Jafari Method (DJM) and the Elzaki Daftardar-Jafari Method (EDJM) to derive approximate analytical solutions. The combination of these methods provides a systematic and efficient approach to addressing the challenges posed by nonlinearities and the memory effects inherent in fractional derivatives. Through illustrative examples, we demonstrate the accuracy and applicability of the proposed methods. The results indicate that DJM and EDJM are powerful tools for solving nonlinear fractional differential equations, offering insights into their underlying dynamics.