Fractional-Order Delay Cobweb Model and Its Price Dynamics

This study compares the price dynamics of a Caputo fractional order delay differential cobweb model with existing cobweb models that have conformable fractional derivatives, Caputo fractional derivatives, and nonsingular kernel fractional derivatives to determine the effect of the time delay parameter on commodity price, besides the positivity of the solution that was investigated. In contrast to previous research, the stability study shows the practical usefulness of our model since the literature’s various time intervals showed short-term equilibrium price convergence but long-term price divergence. The results showed that the time gap between supply and demand accounts for the noise associated with the fractional-order time delay differential cobweb regarding convergence (or divergence), which is nonexistent in the literature models. It is observed in the paper that lower fractional order goes with a higher time delay, while we have the reverse for high fractional order. This depicts the realities of price behaviour in connection with the law of demand and supply of commodities that take a finite period for them to be ready for distribution to the market. It is, therefore, recommended that price adjustment models be modeled using fractional delay differential equations. The numerical simulations were done using MATLAB.