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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Solving the liquid tank system by generalization FAT

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pp. 1497–1502Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2538XML
Received:
01 Nov 2025
Published Online:
27 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2538
Pages:
1497–1502

Abstract

In this work, we presented a generalization of FAT and proved some of the properties of (FAT). Eng. We also derive the FAT of fuzzy derivatives up to the third order and further generalize the said formula for the nth order fuzzy derivative by using the strongly generalized H-differentiability concept. The obtained formulas are then employed to solve the FIVP of a first-order liquid tank system.

Keywords

Subject Classifications

Primary 93A30Secondary 49K15

References

[1] D. V. Widder, “A Simplified Approach To Cauchy’S Integral Theorem,” The American Mathematical Monthly, vol. 53, no. 7, pp. 359–363 (1946).
[2] S. H. Asaad, I. S. Ahmed, and H. H. Ebrahim, “On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring,” Baghdad Sci. J, vol. 19, no. 5, pp. 1148-1154 (2022).
[3] E. Christophe, D. Léger, and C. Mailhes, “Quality criteria benchmark for hyperspectral imagery,” IEEE Transactions on Geoscience and Remote Sensing, vol. 43, no. 9, pp. 2103–2114 (2005).
[4] E. Silverberg, C. C. Boring, and T. S. Squires, “Cancer statistics, 1990,” CA: a cancer journal for clinicians, vol. 40, no. 1, pp. 9–26 (1990).
[5] H. F. Abbas, H. H. Ebrahim, and A. Al-Fayadh, “Soft P*–field and some of its properties,” J. Disc. Math. Sci. Cryptogr, vol. 26, no. 7, pp. 1875–1882 (2023).
[6] G. K. Watugala, “Sumudu transform: A new integral transform to solve differential equations and control engineering problems,” Applied Mathematics and Computation, vol. 24, no. 1, pp. 35–43 (1993).
[7] H. Gündoğdu and Ö. F. Gözükızıl, “Solving nonlinear partial differential equations by using Adomian decomposition method, modified decomposition method and Laplace decomposition method,” MANAS Journal of Engineering, vol. 5, no. 1, pp. 1–13 (2017).
[8] H.-J. Zimmermann, Fuzzy set theory and its applications, 4th ed. Berlin, Germany: Springer Science and Business Media (2001).
[9] W. N. Zhou, “Generalization of L-closure spaces,” Fuzzy Sets and Systems, vol. 149, no. 3, pp. 415–432 (2005).
[10] H. M. Gloster and D. G. Brodland, “The epidemiology of skin cancer,” Dermatologic Surgery, vol. 22, no. 3, pp. 217–226 (1996).
[11] H. Serrano, J. Scotto, G. Shornick, T. R. Fears, and E. R. Greenberg, “Incidence of nonmelanoma skin cancer in New Hampshire and Vermont,” Journal of the American Academy of Dermatology, vol. 24, no. 4, pp. 574–579 (1991).
[12] J. Kaldor, D. Shugg, B. Young, T. Dwyer, and Y. G. Wang, “Non-melanoma skin cancer: ten years of cancer-registry-based surveillance,” International journal of cancer, vol. 53, no. 6, pp. 886–891 (1993).
[13] J. Schiff, The Laplace Transform: Theory and Application. New York, USA: Springer (2013), doi: 10.1007/978-1-4614-4949-7.
[14] A. S. Mohammed, I. S. Ahmed, and S. H. Asaad, “Study of the rings in which each element expresses as the sum of an idempotent and pure,” Int. J. Nonlinear Anal. Appl, vol. 12, no. 2, pp. 1719-1724 (2021), doi: 10.22075/IJNAA.2021.5311.
[15] S. M. Kadham and M. A. Mustafa, “Medical applications of the new-transform,” Journal of Interdisciplinary Mathematics, vol. 26, no. 6, pp. 1341–1353 (2023).
[16] S. M. Kadham and M. A. Mustafa, “Fuzzy SHmath. Mbio-transform generalization and application to skin cancer imaging distributed diseases,” J. Interdiscip. Math, vol. 26, no. 6, pp. 1031–1042 (2023).
[17] S. A. Al-Ameedee and A. J. Obaid, “New results and application of differential quasi subordinations for higher-order derivatives of meromorphic multivalent functions,” Journal of Interdisciplinary Mathematics, vol. 26, no. 4, pp. 643–650 (2023), doi: 10.47974/JIM-1483.
[18] R. H. Hasan, M. A. Kadhim, and A. M. Darweesh, “Fuzzy partial T-transforms applied to a system of PDE,” J. Interdiscip. Math, vol. 26, no. 6, pp. 1099–1107 (2023).

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