Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus
In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When <inline-formula> <math display="inline"> <semantics>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/434 |
| _version_ | 1818289214693834752 |
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| author | Samir Saker Mohammed Kenawy Ghada AlNemer Mohammed Zakarya |
| author_facet | Samir Saker Mohammed Kenawy Ghada AlNemer Mohammed Zakarya |
| author_sort | Samir Saker |
| collection | DOAJ |
| description | In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When <inline-formula> <math 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 Hardy, Copson, Bennett and Leindler inequalities. |
| first_indexed | 2024-12-13T02:08:43Z |
| format | Article |
| id | doaj.art-4284c1be99b44d27955690bc87ab8272 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-13T02:08:43Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4284c1be99b44d27955690bc87ab82722022-12-22T00:03:03ZengMDPI AGMathematics2227-73902020-03-018343410.3390/math8030434math8030434Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable CalculusSamir Saker0Mohammed Kenawy1Ghada AlNemer2Mohammed Zakarya3Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, EgyptDepartment of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh, Saudi 11656, ArabiaDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaIn this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When <inline-formula> <math 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 Hardy, Copson, Bennett and Leindler inequalities.https://www.mdpi.com/2227-7390/8/3/434fractional hardy’s inequalityfractional bennett’s inequalityfractional copson’s inequalityfractional leindler’s inequalitytimescalesconformable fractional calculusfractional hölder inequality |
| spellingShingle | Samir Saker Mohammed Kenawy Ghada AlNemer Mohammed Zakarya Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus Mathematics fractional hardy’s inequality fractional bennett’s inequality fractional copson’s inequality fractional leindler’s inequality timescales conformable fractional calculus fractional hölder inequality |
| title | Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus |
| title_full | Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus |
| title_fullStr | Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus |
| title_full_unstemmed | Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus |
| title_short | Some Fractional Dynamic Inequalities of Hardy’s Type via Conformable Calculus |
| title_sort | some fractional dynamic inequalities of hardy s type via conformable calculus |
| topic | fractional hardy’s inequality fractional bennett’s inequality fractional copson’s inequality fractional leindler’s inequality timescales conformable fractional calculus fractional hölder inequality |
| url | https://www.mdpi.com/2227-7390/8/3/434 |
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