Semi-Analytical Solutions of Fractional Differential Equations in RL and RC Circuits

Fractional-order differential equations provide an effective mathematical model for electrical circuits that exhibit memory and nonlocal effects. This study investigates semi-analytical methods to solve fractional-order differential equations of RL and RC electrical circuits. The semi-analytical methods, namely the Generalized Differential Transform Method (GDTM), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), and Adomian Decomposition Method (ADM), are used to solve equations. The obtained series solutions are analyzed and compared graphically for different values of the fractional-order to illustrate their impact on circuit dynamics. The comparative results provide useful guidance for selecting an appropriate mathematical method for solving fractional-order electrical circuit models.