In this chapter, we present new numerical methods for solving fractional differential equations (FDEs) that involve Caputo-Fabrizio and proportional Caputo derivatives. Initially we focused on solving FDEs involving Caputo-Fabrizio derivatives, utilizing tools from fractional calculus mainly an important decomposition tool viz., the new iterative method, numerical analysis, and fixed point theory. We provide the new algorithm, along with detailed error and stability analyses, and validate the method through simulations compared with the two-step Adams-Bashforth scheme. Later, we introduce a new predictor-corrector method for solving proportional Caputo differential equations of the form \(^{pc}D^{\alpha } v(t) = f_1(t, v(t)), ~~t\ge 0, ~ 0< \alpha < 1\) where \(^{pc}D^{\alpha } v(t)\) represents proportional Caputo derivative and \(f_1\) is a non-linear operator. We also provide error and stability analyses, with several examples illustrating the method’s effectiveness and comparing solution curves to exact solutions.