Comparative Numerical Results Considering Fractional Derivative and Memory Dependent Derivative in Modeling RL and RC Electrical Circuits

Abstract

This chapter presents a comparative study between the old and new fractional Caputo derivatives with power-law and exponential kernel and a memory- dependent derivative in modeling electrical circuits such as RL and RC circuits with a time-dependent source. The integer order derivative is generalized by both derivatives: Caputo and memory-dependent derivatives. Employing the governing derivatives mentioned above, we numerically investigated the solution of the obtained equations and compared the results. Interestingly, the results showed the existence of heterogeneities in the circuit that caused irreversible effects, such as dissipation. However, it is found that, though the fractional derivative shows an interesting effect on the system, the memory- dependent derivative exhibits different complexity because it provides more access into memory effects and could be a better model in analyzing the physical system.