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Research Article | Open Access

On Hilbert-Pachpatte type inequalities within ψ-Hilfer fractional generalized derivatives

Yasemin Başcı1( ), Dumitru Baleanu2,3,4
Bolu Abant Izzet Baysal University, Department of Mathematics, Faculty of Arts and Sciences, Golkoy 14280, Bolu, Turkey
Çankaya University, Department of Mathematics, Faculty of Arts and Sciences, Ankara 06530, Turkey
Lebanese American University, Beirut, Lebanon
Institutes of Space Sciences Magurele-Bucharest, Romania
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Abstract

In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided ψ-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 ψ-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting ψ, a 1 , b 1 and considering the limit of the parameters α and β.

Keywords

Hilbert-Pachpatte type inequalityψ-Hilfer fractional derivativeRiemann-Liouville derivativehomogeneous kernelfractional derivative
CLC number: 26A24, 26A33, 26B15

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 14008-14026
DOI: 10.3934/math.2023716

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Cite this article:
Başcı Y, Baleanu D. On Hilbert-Pachpatte type inequalities within ψ-Hilfer fractional generalized derivatives. AIMS Mathematics, 2023, 8(6): 14008-14026. https://doi.org/10.3934/math.2023716

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Received: 27 December 2022
Revised: 30 March 2023
Accepted: 03 April 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)