  This working paper presents a comprehensive study on the development and
analysis of various electricity market models, focusing on continuous,
discrete, and fractional-order approaches. The continuous model captures the
ongoing interactions between power producers and consumers using differential
equations, providing insights into long-term trends and steady-state behaviors.
The discrete model, suitable for analyzing scenarios where market events occur
at specific time intervals, incorporates memory effects to account for
historical behaviors and decisions, offering a realistic representation of
short-term market dynamics. The fractional-order model introduces fractional
calculus to capture memory effects and hereditary properties, enhancing the
model's realism and predictive capability by reflecting the influence of past
states on current market behavior.
