Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators

Muhammad Kaurangini; Umar Muhammad Abubakar; Enes Ata

doi:10.47000/tjmcs.1545292

Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators

Abstract

Unified Mittag-Leffler function defined by using beta function that consist of two Fox-Wright function in its kernel is introduced and its relation to Fox-Wright, Fox-$H$ functions and Mellin-Barnes type integral are illustrate. The beta, SUM, Laplace, Whittaker, $K$- and $P_{\partial}$- integral transforms are applied to the function and generalized formulas are obtained in form of both unified Mittag-Leffler and Fox-Wright functions. The convergence and differential formulas of this unified Mittag-Leffler function is also demonstrated.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Muhammad Kaurangini
0000-0001-9144-9433
Nigeria

Umar Muhammad Abubakar ^*
0000-0003-3935-4829
Nigeria

Enes Ata
0000-0001-6893-8693
Türkiye

Publication Date

December 30, 2025

Submission Date

September 8, 2024

Acceptance Date

October 6, 2025

Published in Issue

Year 2025 Volume: 17 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1545292

IZ

https://izlik.org/JA67UN69TY

Cite

RIS / Bibtex

APA

Kaurangini, M., Abubakar, U. M., & Ata, E. (2025). Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators. Turkish Journal of Mathematics and Computer Science, 17(2), 534-543. https://doi.org/10.47000/tjmcs.1545292

AMA

1.Kaurangini M, Abubakar UM, Ata E. Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators. TJMCS. 2025;17(2):534-543. doi:10.47000/tjmcs.1545292

Chicago

Kaurangini, Muhammad, Umar Muhammad Abubakar, and Enes Ata. 2025. “Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators”. Turkish Journal of Mathematics and Computer Science 17 (2): 534-43. https://doi.org/10.47000/tjmcs.1545292.

EndNote

Kaurangini M, Abubakar UM, Ata E (December 1, 2025) Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators. Turkish Journal of Mathematics and Computer Science 17 2 534–543.

IEEE

[1]M. Kaurangini, U. M. Abubakar, and E. Ata, “Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators”, TJMCS, vol. 17, no. 2, pp. 534–543, Dec. 2025, doi: 10.47000/tjmcs.1545292.

ISNAD

Kaurangini, Muhammad - Abubakar, Umar Muhammad - Ata, Enes. “Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators”. Turkish Journal of Mathematics and Computer Science 17/2 (December 1, 2025): 534-543. https://doi.org/10.47000/tjmcs.1545292.

JAMA

1.Kaurangini M, Abubakar UM, Ata E. Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators. TJMCS. 2025;17:534–543.

MLA

Kaurangini, Muhammad, et al. “Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 2, Dec. 2025, pp. 534-43, doi:10.47000/tjmcs.1545292.

Vancouver

1.Muhammad Kaurangini, Umar Muhammad Abubakar, Enes Ata. Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators. TJMCS. 2025 Dec. 1;17(2):534-43. doi:10.47000/tjmcs.1545292