On Hilbert-Pachpatte type inequalities within $ \psi $-Hilfer fractional generalized derivatives-Reference-Cited by-同舟云学术

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

Published:2023 Issue:6 Volume:8 Page:14008-14026
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Başcı Yasemin¹,Baleanu Dumitru²³⁴

Affiliation:

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

Abstract

<abstract><p>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 <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. 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 $.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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