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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 2

Five-parameter discrete Mittag-Leffler function and corresponding discrete double fractional operator

Mehmet Ali Özarslan(EASTERN MEDITARRANEAN UNIVERSITY)0000-0002-6473-9299
Cemaliye Kürt(FINAL INTERNATIONAL UNIVERSITY)0000-0002-5559-3849
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)

We also obtain the left inverse operator which is the corresponding discrete difference operator for the discrete double fractional operator.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In recent years, discrete Mittag-Leffler (ML) functions have been investigated intensively since they are connected with the discrete fractional calculus and have interesting applications in applied sciences.
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Key Findings & Data:In this study, inspired by the five-parameter ML function by Özarslan et al. [16], we define its discrete version, namely five-parameter discrete ML function.
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Conclusion & Impact:We also obtain the left inverse operator which is the corresponding discrete difference operator for the discrete double fractional operator.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:discrete ML functions · discrete fractional sums · discrete fractional differences

Abstract

In recent years, discrete Mittag-Leffler (ML) functions have been investigated intensively since they are connected with the discrete fractional calculus and have interesting applications in applied sciences. In this study, inspired by the five-parameter ML function by Özarslan et al. [16], we define its discrete version, namely five-parameter discrete ML function. We explore various characteristics, such as the double fractional sum and difference, of the discrete ML function with five parameters. Then, using the mentioned discrete function, we introduce the discrete double fractional operator having this function through the semigroup property. We also obtain the left inverse operator which is the corresponding discrete difference operator for the discrete double fractional operator.

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Cite This Article

Özarslan, M. A., Kürt, C. (2025). Five-parameter discrete Mittag-Leffler function and corresponding discrete double fractional operator. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 2. https://doi.org/10.15672/hujms.1632946

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