On Hilbert-Pachpatte type inequalities within $ \psi $-Hilfer fractional generalized derivatives

Yasemin Başcı; Dumitru Baleanu; Yasemin Başcı; Dumitru Baleanu

doi:10.3934/math.2023716

AIMS Mathematics

2023, Volume 8, Issue 6: 14008-14026. doi: 10.3934/math.2023716

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Research article

On Hilbert-Pachpatte type inequalities within $ \psi $-Hilfer fractional generalized derivatives

Yasemin Başcı ^{1
,
,},
Dumitru Baleanu ^2,3,4

1.
Bolu Abant Izzet Baysal University, Department of Mathematics, Faculty of Arts and Sciences, Golkoy 14280, Bolu, Turkey
2.
Çankaya University, Department of Mathematics, Faculty of Arts and Sciences, Ankara 06530, Turkey
3.
Lebanese American University, Beirut, Lebanon
4.
Institutes of Space Sciences Magurele-Bucharest, Romania

Received: 27 December 2022 Revised: 30 March 2023 Accepted: 03 April 2023 Published: 14 April 2023
MSC : 26A24, 26A33, 26B15

In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided $ \psi $-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pečarić and Vuković ^[1]. Furthermore, using the specific cases of the $ \psi $-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting $ \psi $, $ a_1 $, $ b_1 $ and considering the limit of the parameters $ \alpha $ and $ \beta $.
- Hilbert-Pachpatte type inequality,
- $ \psi $-Hilfer fractional derivative,
- Riemann-Liouville derivative,
- homogeneous kernel,
- fractional derivative
Citation: Yasemin Başcı, Dumitru Baleanu. On Hilbert-Pachpatte type inequalities within $ \psi $-Hilfer fractional generalized derivatives[J]. AIMS Mathematics, 2023, 8(6): 14008-14026. doi: 10.3934/math.2023716

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Abstract

In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided $ \psi $-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pečarić and Vuković ^[1]. Furthermore, using the specific cases of the $ \psi $-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting $ \psi $, $ a_1 $, $ b_1 $ and considering the limit of the parameters $ \alpha $ and $ \beta $.

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