Analysis of fractional circuits using integral RT

Abstract

Many engineering and physical systems are characterized by the existence of memory and hereditary features that impose a limitation on the traditional models. Fractional calculus is a powerful tool in which memory can be naturally introduced. However, analytical solutions of nonlinear fractional differential equations are still challenging. In this work, an integral Rohit Transform (RT) is introduced for the purpose of solving nonlinear memory systems as well as fractional electrical circuits. The basic characteristics of the transform are established and then utilized in the cases of nonlinear oscillators and the graphenebased fractional RC model. Analytical and semi-analytical closed-form solutions in terms of Mittag-Leffler functions are attained. Stability as well as physical meanings are argued. The analytical solutions obtained using the integral Rohit Transform (IRT) and Adomian Decomposition Method (ADM) are further illustrated through numerical simulations. Three-dimensional response surfaces and memory kernel plots demonstrate the influence of the fractional order and nonlinear memory effects on the system dynamics. The numerical results are consistent with the theoretical analysis and confirm the effectiveness of the proposed RT-based approach for solving nonlinear fractional memory systems. Results indicate that the Integral Rohit transform both simplifies algebraic manipulation and provides a better memory representation.