Survey on Circuit-Based Fractal Computation

This abstract investigates the Recursive Two-Circuit Series Analogue Fractance Circuit, local fractional calculus, and nonlocal fractal integro-differential equations within the domain of circuit-based fractal computation. Circuit-based fractal models exhibit superior flexibility in capturing complex patterns compared to conventional methods. Local fractional calculus extends classical calculus to address fractal-related problems, exemplified by the local fractional diffusion equation. Nonlocal Fractal Integro-Differential Equations combine nonlocal calculus and fractal geometry to address practical challenges. The Recursive Two-Circuit Series Analogue Fractance Circuit, featuring a self-referential structure, emulates fractional calculus in electrical systems. Applications encompass solving fractional diffusion equations in fractal media, mathematical modeling, signal processing, data analysis, and advection-dispersion models, particularly in the context of transport process modeling associated with anomalous diffusion and fractal dimensions.