Fractional interactive fuzzy $ F $-correlated Caputo-Katugampola differential equations

Weiqi Ding; Haibo Gu; Yan Chen; Weiqi Ding; Haibo Gu; Yan Chen

doi:10.3934/era.2026060

Electronic Research Archive

2026, Volume 34, Issue 2: 1315-1341. doi: 10.3934/era.2026060

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Fractional interactive fuzzy $ F $-correlated Caputo-Katugampola differential equations

1.
School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China
2.
School of Mathematics Sciences, Xinjiang Normal University, Urumqi 830017, China
3.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250000, China

Received: 24 November 2025 Revised: 26 January 2026 Accepted: 03 February 2026 Published: 09 February 2026

In this paper, we investigated the existence and uniqueness of solutions for a class of interactive fuzzy Caputo–Katugampola $ F $-correlated fractional differential equations with time delay. First, we gave the definition of the correlated integral and derivative for interactive fuzzy Caputo–Katugampola $ F $-correlated systems. Second, we presented an equivalent integral formulation and, under suitable assumptions, established the existence of solutions to fuzzy interactive Caputo–Katugampola $ F $-correlated fractional-order differential equations with time delay by applying Schauder's fixed-point theorem. Finally, a numerical example was presented to validate the effectiveness of the proposed approach.
- interactive derivative,
- $ F $-correlated fuzzy processes,
- fuzzy fractional differential equations,
- time delay
Citation: Weiqi Ding, Haibo Gu, Yan Chen. Fractional interactive fuzzy $ F $-correlated Caputo-Katugampola differential equations[J]. Electronic Research Archive, 2026, 34(2): 1315-1341. doi: 10.3934/era.2026060

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Abstract

In this paper, we investigated the existence and uniqueness of solutions for a class of interactive fuzzy Caputo–Katugampola $ F $-correlated fractional differential equations with time delay. First, we gave the definition of the correlated integral and derivative for interactive fuzzy Caputo–Katugampola $ F $-correlated systems. Second, we presented an equivalent integral formulation and, under suitable assumptions, established the existence of solutions to fuzzy interactive Caputo–Katugampola $ F $-correlated fractional-order differential equations with time delay by applying Schauder's fixed-point theorem. Finally, a numerical example was presented to validate the effectiveness of the proposed approach.

References

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