Fuzzy discrete fractional granular calculus and its application to fractional cobweb models

Xuelong Liu, Guoju Ye, Wei Liu and Fangfang Shi

Applied Mathematics and Computation, 2025, vol. 489, issue C

Abstract: This work aims to solve a fuzzy initial value problem for fractional difference equations and to study a class of discrete fractional cobweb models with fuzzy data under the Caputo granular difference operator. Based on relative-distance-measure fuzzy interval arithmetic, we first present several new concepts for fuzzy functions in the field of fuzzy discrete fractional calculus, such as the forward granular difference operator, Riemann-Liouville fractional granular sum, Riemann-Liouville and Caputo granular differences. The composition rules and Leibniz laws used to solve a fuzzy initial value problem for fractional difference equations are also presented. As applications, we obtain the solutions of fuzzy discrete Caputo fractional cobweb models, provide conditions for the convergence of the solution to the equilibrium value, and discuss different cases of how the trajectory of the granular solution converges to the equilibrium value. The developed results are also illustrated through several numerical examples.

Keywords: Granular difference; Discrete fractional calculus; Cobweb model (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324006374
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006374

DOI: 10.1016/j.amc.2024.129176

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().