Fractional Reverse Coposn's Inequalities via Conformable Calculus on Time Scales

被引：20

作者：

Zakarya, Mohammed ^{[1
,2
]}

Altanji, Mohamed ^{[1
]}

AlNemer, Ghada ^{[3
]}

Abd El-Hamid, Hoda A. ^{[4
]}

Cesarano, Clemente ^{[5
]}

Rezk, Haytham M. ^{[6
]}

机构：

[1] King Khalid Univ, Coll Sci, Dept Math, POB 9004, Abha 61413, Saudi Arabia

[2] Al Azhar Univ, Fac Sci, Dept Math, Assiut 71524, Egypt

[3] Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 105862, Riyadh 11656, Saudi Arabia

[4] Beni Suef Univ, Fac Sci, Dept Math & Comp Sci, Bani Suwayf 62511, Egypt

[5] Univ Telemat Int Uninettuno, Sect Math, I-00186 Rome, Italy

[6] Al Azhar Univ, Fac Sci, Dept Math, Nasr City 11884, Egypt

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 04期

关键词：

Copson’ s inequality; Hö lder’ time scales; conformable fractional calculus; DYNAMIC INEQUALITIES; HARDY-TYPE; HILBERT;

D O I：

10.3390/sym13040542

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson's type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Holder's inequality, and integration by parts on fractional time scales. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues. In addition, when alpha = 1, we obtain some well-known time scale inequalities due to Hardy, Copson, Bennett, and Leindler inequalities.

引用

页数：16

共 34 条

[1] Dynamic Inequalities in Quotients with General Kernels and Measures [J].

Abd El-Hamid, H. A. ;

Rezk, H. M. ;

Ahmed, A. M. ;

AlNemer, Ghada ;

Zakarya, M. ;

El Saify, H. A. .

JOURNAL OF FUNCTION SPACES, 2020, 2020

[2] On conformable fractional calculus [J].

Abdeljawad, Thabet .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 :57-66

[3] Some Dynamic Inequalities of Hilbert's Type [J].

Ahmed, A. M. ;

AlNemer, Ghada ;

Zakarya, M. ;

Rezk, H. M. .

JOURNAL OF FUNCTION SPACES, 2020, 2020

[4]

Ahmed A.M, 2020, J DCDIS A

[5] Some Dynamic Hilbert-Type Inequalities on Time Scales [J].

AlNemer, Ghada ;

Zakarya, Mohammed ;

Abd El-Hamid, Hoda A. ;

Agarwal, Praveen ;

Rezk, Haytham M. .

SYMMETRY-BASEL, 2020, 12 (09)

[6] Dynamic Hardy-type inequalities with non-conjugate parameters [J].

AlNemer, Ghada ;

Zakarya, M. ;

Abd El-Hamid, H. A. ;

Kenawy, M. R. ;

Rezk, H. M. .

ALEXANDRIA ENGINEERING JOURNAL, 2020, 59 (06) :4523-4532

[7] A conformable fractional calculus on arbitrary time scales [J].

Benkhettou, Nadia ;

Hassani, Salima ;

Torres, Delfim F. M. .

JOURNAL OF KING SAUD UNIVERSITY SCIENCE, 2016, 28 (01) :93-98

[8] SOME ELEMENTARY INEQUALITIES .2. [J].

BENNETT, G .

QUARTERLY JOURNAL OF MATHEMATICS, 1988, 39 (156) :385-400

[9] SOME ELEMENTARY INEQUALITIES [J].

BENNETT, G .

QUARTERLY JOURNAL OF MATHEMATICS, 1987, 38 (152) :401-425

[10] The best constant in a fractional Hardy inequality [J].

Bogdan, Krzysztof ;

Dyda, Bartlomiej .

MATHEMATISCHE NACHRICHTEN, 2011, 284 (5-6) :629-638

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