New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators

Shuang-Shuang Zhou; Saima Rashid; Saima Parveen; Ahmet Ocak Akdemir; Zakia Hammouch; Shuang-Shuang Zhou; Saima Rashid; Saima Parveen; Ahmet Ocak Akdemir; Zakia Hammouch

doi:10.3934/math.2021267

AIMS Mathematics

2021, Volume 6, Issue 5: 4507-4525. doi: 10.3934/math.2021267

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New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators

1.
School of Science, Hunan City University, Yiyang 413000, P. R. China
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, Agri Ibrahim Cecen University, Agri. Turkey
4.
Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

Received: 04 December 2020 Accepted: 08 February 2021 Published: 22 February 2021
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

In this work, a new strategy to derive inequalities by employing newly proposed fractional operators, known as a Hilfer generalized proportional fractional integral operator ($ \widehat{\mathcal{GPFIO}} $). The presented work establishes a relationship between weighted extended Čebyšev version and Pólya-Szegö type inequalities, which can be directly used in fractional differential equations and statistical theory. In addition, the proposed technique is also compared with the existing results. This work is important and timely for evaluating fractional operators and predicting the production of numerous real-world problems in varying nature.
- integral inequality,
- $ \Lambda $-generalized proportional fractional integral,
- Čebyšev inequality,
- Pólya-Szegö inequality
Citation: Shuang-Shuang Zhou, Saima Rashid, Saima Parveen, Ahmet Ocak Akdemir, Zakia Hammouch. New computations for extended weighted functionals within the Hilfer generalized proportional fractional integral operators[J]. AIMS Mathematics, 2021, 6(5): 4507-4525. doi: 10.3934/math.2021267

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Abstract

In this work, a new strategy to derive inequalities by employing newly proposed fractional operators, known as a Hilfer generalized proportional fractional integral operator ($ \widehat{\mathcal{GPFIO}} $). The presented work establishes a relationship between weighted extended Čebyšev version and Pólya-Szegö type inequalities, which can be directly used in fractional differential equations and statistical theory. In addition, the proposed technique is also compared with the existing results. This work is important and timely for evaluating fractional operators and predicting the production of numerous real-world problems in varying nature.

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