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Journals / Turkish Journal of Mathematics and Computer Science / 2025 / Volume: 17 Issue: 2

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

Muhammad Kaurangini(Aliko Dangote University of Science and Technology, Wudil P.M.B.: 3244 Kano, Kano State-NIGERIA)0000-0001-9144-9433
Umar Muhammad Abubakar(Aliko Dangote University of Science and Technology,\\ Wudil P.M.B.: 3244 Kano, Kano State-NIGERIA)0000-0003-3935-4829
Enes Ata(Ahi Evran University, Kirsehir, TURKEY)0000-0001-6893-8693
Pages
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Publication Date
2025-12-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The convergence and differential formulas of this unified Mittag-Leffler function is also demonstrated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:The convergence and differential formulas of this unified Mittag-Leffler function is also demonstrated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Mittag-Leffler function · Q Function · Fox-Wright function

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.

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Cite This Article

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, Volume: 17 Issue: 2. https://doi.org/10.47000/tjmcs.1545292

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