Mathematics

Cobweb models with Hilfer nabla fractional differences

H. C. Koyuncuoğlu^a, Ö. Öztunç Kaymak^b, J. M. Jonnalagadda<sup>c

a</sup> Izmir Katip Celebi University, Izmir, Türkiye
^b Izmir Democracy University, Izmir, Türkiye
^c Birla Institute of Technology and Science Pilani, Hyderabad, India

Abstract: We concentrate on the discrete fractional cobweb models involving generalized fractional differences in the sense of Hilfer. Hilfer fractional differences are introduced as an extension of Riemann–Liouville and Caputo fractional differences. In the construction of the discrete fractional cobweb model, we employ Hilfer nabla fractional difference and we define two models which involve Hilfer nabla fractional difference on demand and supply function, respectively. We solve the proposed models due to Laplace transform, and also, we analyze the asymptotic behaviour of the solutions. After applying the proven theorems to an example with appropriate parameters, these results are verified for different solutions of the cobweb models containing Riemann–Liouville, Caputo, and Hilfer nabla fractional differences.

Keywords: cobweb model, Hilfer nabla difference, Mittag-Leffler function, discrete fractional Laplace transform.

UDC: 517.962.2

Received: 16.04.2024
Revised: 05.04.2025

Language: English

DOI: 10.47475/2500-0101-2025-10-3-541-551