<p>This work outlines a powerful adaptation of the Haar wavelet and cuckoo search optimization algorithm within the framework of Atangana’s beta derivative. This method uses the Haar wavelet basis function with a beta fractional integral operator to derive a new operational matrix of integration that transforms the model into an objective function with undetermined coefficients. The undetermined coefficients are optimized by using the cuckoo search optimization (CSO) algorithm, which is a metaheuristic computational algorithm based on the breeding behavior of cuckoo species in nature. It is an efficient computing algorithm for optimizing problems with the ability to converge rapidly towards the best solution. The developed methodology is tested on a generalized electronic circuit model considering RL, RC, and nonlinear RC circuit models as subcases, analyzed numerically, and analogized with exact and Runge-Kutta method. An analog simulation is conducted in Multisim and compared with the numerical results. The error analysis comprised mean absolute error, maximum absolute error, and experimental convergence rate. These have been evaluated and documented elaborately, indicating minimal error and thereby confirming the suitability of the method. Besides, a comprehensive statistical analysis involving root mean square error, Theil’s inequality coefficient, mean absolute deviation, and Nash-Sutcliffe efficiency coefficient adds further strength to the validity of the method.</p>