Stability of Cobweb economic model involving Hilfer fractional derivative

TL;DR

This paper investigates the stability of cobweb economic models incorporating Hilfer fractional derivatives, comparing it with Caputo and Riemann-Liouville derivatives through theoretical derivations and numerical illustrations.

Contribution

It introduces a novel analysis of cobweb models using Hilfer fractional derivatives and compares its advantages over traditional fractional derivatives.

Findings

Hilfer derivative offers stability benefits over Caputo and Riemann-Liouville derivatives.

Numerical examples demonstrate the effectiveness of the Hilfer derivative in modeling.

Graphical analysis supports the theoretical advantages of Hilfer derivatives.

Abstract

This paper evaluates the solution of cobweb models when there is a Hilfer fractional derivative in the demand and supply function. Particular cases when Hilfer derivative reducing to Caputo and Riemann-Liouville derivative are discussed. Subsequently, the solution of the cobweb model with Riemann-Liouville derivative is derived instantly. Two numerical examples interpreting the crafted theory is deliberated with illustrations and comparisons. Conclusions based on the graphical illustrations is outlined in detail. These illustrations highlight the advantage of the Hilfer fractional derivative over the other two fractional derivatives.