Employing effective solution methods for Caputo-based sequential fractional models

This paper investigates a class of nonlinear sequential singular fractional differential equations (FDEs) involving Caputo derivatives. This type of equation has several key advantages that enhance its value, such as capturing memory and hereditary effects. Viscoelastic materials and anomalous diffusion, as well as biological systems, can take advantage of this feature. In addition, fractional derivatives possess a sequential structure that enables the implementation of multiscale processes and hierarchical memory responses. Moreover, it provides an effective and flexible framework for solving differential equations compared to classical differential equations. It can therefore be used to model complex systems in physics, biology, and engineering. As an example, it can provide a more precise description of subdiffusion or superdiffusion in diffusion processes. As a result, it accounts for delayed responses and non-uniform actuation effects in control systems.