Numerical Analysis of a Class of Fractional-Order Nonlinearity Anomalous Subdiffusion Systems

Many natural phenomena, such as physical, chemical, and biological processes, can be described using n-coupled nonlinearity anomalous subdiffusion systems. Furthermore, fractional differential equations are a useful tool for modeling practical problems in science because they allow for the incorporation of infinite memory through the consideration of previous states. This paper proposes numerical and analytical techniques for studying n-coupled fractional-order nonlinearity anomalous subdiffusion systems, including the construction of improved implicit difference methods and the discussion of stability and convergence using energy methods. The stability and convergence conditions are determined based on different implicit methods. The obtained conditions are related to the system dimension n. The effectiveness of the theoretical results is demonstrated using two numerical examples.