Multi-step reproducing kernel algorithm for solving Caputo–Fabrizio fractional stiff models arising in electric circuits

Electrical engineering models can typically be simulated with a circuit of interconnected electrical components containing electrically charged particles that can be moved from atom to atom across a closed conducting pathway. In this paper, the electric circuit model of fractional stiff differential equations is investigated using a novel multi-step approach of reproducing kernel method (MS-RKM). Fractional operator with non-singular kernel, Caputo-Fabrizio fractional derivative, is considered to obtain accurate approximate solutions over a sequence of intervals for the fractional stiff system. To maintain dimensionality of the physical parameters appearing in the electrical circuit, a parameter is used to characterize the presence of fractional structures in the electrical model. Solving our model, in the context of classic numerical methods, is a difficult task, and solutions are often offered in a very small region with a very slow rate of convergence or they may diverge in wider regions. MS-RKM is treated as a new modification of RKM on subintervals, which considerably reduces the number of arithmetic operations and thus time and effort to get approximate solutions. Efficiency, simplicity, and accuracy of the proposed multi-step approach in solving the fractional stiff system is evident through numerical simulations performed for RL, RC, and RLC circuit models.