New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales
Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math><...
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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/3de11f4e239944e5b1ca8714b0416f71 |
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| Summary: | Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable dynamic inequalities of Steffensen-type on time scales. In the case when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we obtain some well-known time scale inequalities due to Steffensen inequalities. For some specific time scales, we further show some relevant inequalities as special cases: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable integral inequalities and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. |
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