In this work, we propose a dynamic cobweb-type market equilibrium model where supply responds to price using a Mittag–Leffler kernel generalized weighted Caputo fractional derivative. By permitting independent fractional orders, a time-varying weight function that reweights historical data, and a monotone economic-time transformation that captures heterogeneous adjustment speeds, the formulation expands upon previous fractional cobweb models. We begin by highlighting several special cases encompassed by our proposed model. Next, we establish well-posedness, covering existence, uniqueness, and continuous dependence on initial data and parameters via an equivalent Volterra integral formulation, alongside a positivity theorem that ensures prices remain economically meaningful. Then, we derive stability conditions for the perturbation dynamics and characterize the constant equilibrium price. To perform the simulation, we constructed an explicit Volterra partition scheme specifically designed for the generalized kernel and established its convergence. In addition, we validated this approach using numerical examples illustrating how fractional orders, weights, and time transformations cause transient oscillations and convergence toward equilibrium.
Madani et al. (Sat,) studied this question.