In this study, numerical approximation of electrical circuits in terms of Caputo fractional time derivative was examined. The order of the derivative being considered was. Haar Wavelet numerical scheme was used to derive the solutions of the fractional electrical circuits, namely RC, LC and RLC. The comparative analysis of numerical simulation of each equation with the classical ones was also provided.

An approximate-analytical method known as Reduced Differential Transform Method (RDTM) is proposed to approximate the Fractional Kolmogorov- Petrovskii –Piskunov Equations. It is a powerful and convenient approximation analytical tool used for linear and nonlinear equations related to various science, engineering and industrial applications. Some illustrative examples are given to exemplify the competence of the proposed scheme and provide precise solutions for nonlinear problems. In addition, a comparison with the classical equation and Homotopy perturbation method illustrates the competency of the technique. The results show that the proposed technique requires minimum computational cost at rapid convergence. This method can be applied to other partial differential equations of fractional order for the analysis of their solutions.