Bounds for certain function related to the incomplete Fox-Wright function

Khaled Mehrez; Abdulaziz Alenazi; Khaled Mehrez; Abdulaziz Alenazi

doi:10.3934/math.2024929

AIMS Mathematics

2024, Volume 9, Issue 7: 19070-19088. doi: 10.3934/math.2024929

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Research article

Bounds for certain function related to the incomplete Fox-Wright function

Khaled Mehrez ¹,
Abdulaziz Alenazi ^{2
,
,}

1.
Department of Mathematics, Kairouan Preparatory Institute for Engineering Studies, University of Kairouan, Kairouan, Tunisia
2.
Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia

Received: 23 January 2024 Revised: 22 April 2024 Accepted: 28 April 2024 Published: 07 June 2024
MSC : 25D15, 26D15, 30C45, 30D15, 33E20

Motivated by the recent investigations of several authors, the main aim of this article is to derive several functional inequalities for a class of functions related to the incomplete Fox-Wright functions that were introduced and studied recently. Moreover, new functional bounds for functions related to the Fox-Wright function are deduced. Furthermore, a class of completely monotonic functions related to the Fox-Wright function is given. The main mathematical tools used to obtain some of the main results are the monotonicity patterns and the Mellin transform for certain functions related to the two-parameter Mittag-Leffler function. Several potential applications for this incomplete special function are mentioned.
- Fox-Wright function,
- incomplete Fox-Wright function,
- Mittag-Leffler function,
- functional inequalities
Citation: Khaled Mehrez, Abdulaziz Alenazi. Bounds for certain function related to the incomplete Fox-Wright function[J]. AIMS Mathematics, 2024, 9(7): 19070-19088. doi: 10.3934/math.2024929

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Abstract

Motivated by the recent investigations of several authors, the main aim of this article is to derive several functional inequalities for a class of functions related to the incomplete Fox-Wright functions that were introduced and studied recently. Moreover, new functional bounds for functions related to the Fox-Wright function are deduced. Furthermore, a class of completely monotonic functions related to the Fox-Wright function is given. The main mathematical tools used to obtain some of the main results are the monotonicity patterns and the Mellin transform for certain functions related to the two-parameter Mittag-Leffler function. Several potential applications for this incomplete special function are mentioned.

References

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