Stability Analysis of Fractional Fuzzy Integral Equations

Rahim Shah; Natasha Irshad; Hajra Imtiaz Abbasi

Stability Analysis of Fractional Fuzzy Integral Equations

Abstract

In this paper, we examine the stability properties of fractional fuzzy integral equations. By employing Banach’s fixed point theorem alongside the Bielecki metric, we derive new results concerning Hyers--Ulam stability and Hyers--Ulam--Rassias stability. The proofs rely essentially on these two analytical tools. To highlight the significance of our findings, three detailed examples are included at the end.

Keywords

Banach fixed point theorem, Bielecki metric, Hyers--Ulam--Rassias stability, Hyers--Ulam stability, Fractional fuzzy integral equations

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Rahim Shah ^*
0009-0001-9044-5470
Pakistan

Natasha Irshad
0009-0008-8166-6520
Pakistan

Hajra Imtiaz Abbasi This is me
0009-0001-4528-2246
Pakistan

Early Pub Date

December 29, 2025

Publication Date

December 29, 2025

Submission Date

December 1, 2025

Acceptance Date

December 18, 2025

Published in Issue

Year 2025 Volume: 1 Number: 1

IZ

https://izlik.org/JA48SS57GK

APA

Shah, R., Irshad, N., & Abbasi, H. I. (2025). Stability Analysis of Fractional Fuzzy Integral Equations. Sakarya Journal of Mathematics, 1(1), 7-15. https://izlik.org/JA48SS57GK

AMA

1.Shah R, Irshad N, Abbasi HI. Stability Analysis of Fractional Fuzzy Integral Equations. Sakarya Journal of Mathematics. 2025;1(1):7-15. https://izlik.org/JA48SS57GK

Chicago

Shah, Rahim, Natasha Irshad, and Hajra Imtiaz Abbasi. 2025. “Stability Analysis of Fractional Fuzzy Integral Equations”. Sakarya Journal of Mathematics 1 (1): 7-15. https://izlik.org/JA48SS57GK.

EndNote

Shah R, Irshad N, Abbasi HI (December 1, 2025) Stability Analysis of Fractional Fuzzy Integral Equations. Sakarya Journal of Mathematics 1 1 7–15.

IEEE

[1]R. Shah, N. Irshad, and H. I. Abbasi, “Stability Analysis of Fractional Fuzzy Integral Equations”, Sakarya Journal of Mathematics, vol. 1, no. 1, pp. 7–15, Dec. 2025, [Online]. Available: https://izlik.org/JA48SS57GK

ISNAD

Shah, Rahim - Irshad, Natasha - Abbasi, Hajra Imtiaz. “Stability Analysis of Fractional Fuzzy Integral Equations”. Sakarya Journal of Mathematics 1/1 (December 1, 2025): 7-15. https://izlik.org/JA48SS57GK.

JAMA

1.Shah R, Irshad N, Abbasi HI. Stability Analysis of Fractional Fuzzy Integral Equations. Sakarya Journal of Mathematics. 2025;1:7–15.

MLA

Shah, Rahim, et al. “Stability Analysis of Fractional Fuzzy Integral Equations”. Sakarya Journal of Mathematics, vol. 1, no. 1, Dec. 2025, pp. 7-15, https://izlik.org/JA48SS57GK.

Vancouver

1.Rahim Shah, Natasha Irshad, Hajra Imtiaz Abbasi. Stability Analysis of Fractional Fuzzy Integral Equations. Sakarya Journal of Mathematics [Internet]. 2025 Dec. 1;1(1):7-15. Available from: https://izlik.org/JA48SS57GK