Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator
In this article, first, we deduce an equality involving the Atangana–Baleanu (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">AB</mi></semantics></math></inl...
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| Main Authors: | , , , , , |
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| Format: | article |
| Language: | EN |
| Published: |
MDPI AG
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/ae822c9f8f044b7dac2de6d769d34e54 |
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| Summary: | In this article, first, we deduce an equality involving the Atangana–Baleanu (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">AB</mi></semantics></math></inline-formula>)-fractional integral operator. Next, employing this equality, we present some novel generalization of Ostrowski type inequality using the Hölder inequality, the power-mean inequality, Young’s inequality, and the Jensen integral inequality for the convexity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><mi mathvariant="sans-serif">Υ</mi><mo>|</mo></mrow></semantics></math></inline-formula>. We also deduced some new special cases from the main results. There exists a solid connection between fractional operators and convexity because of their fascinating properties in the mathematical sciences. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. It is assumed that the results presented in this article will show new directions in the field of fractional calculus. |
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