Fractional derivative of demand and supply functions in the cobweb economics model and Markov process

Abstract

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This paper presents a more general cobweb model that incorporates the Hilfer fractional derivative in either the demand or supply function or Markov process. The main contributions of this study include deriving the analytical solution for the general model, analyzing the stability of the solution, introducing the equilibrium position using Mittag–Leffler functions, and providing detailed graphical illustrations to validate the effectiveness of the proposed model. The outcomes generalize some known results.

Keywords

• cobweb model
• Hilfer fractional derivative
• demand and supply functions
• Mittag–Leffler function
• Markov process