ON RESULTS OF MIDPOINT-TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL OPERATORS WITH TWICE-DIFFERENTIABLE FUNCTIONS

被引：0

作者：

Hezenci, Fatih ^{[1
]}

Budak, Huseyin ^{[1
]}

机构：

[1] Duzce Univ, Fac Sci & Arts, Dept Math, TR-81620 Duzce, Turkiye

来源：

HONAM MATHEMATICAL JOURNAL | 2023年 / 45卷 / 02期

关键词：

midpoint-type inequality; fractional conformable integrals; fractional conformable derivatives; fractional calculus; convex function; HERMITE-HADAMARD; REAL NUMBERS; INTEGRALS; MAPPINGS;

D O I：

10.5831/HMJ.2023.45.2.340

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article establishes an equality for the case of twice -differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint -type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are ob-tained by taking advantage of the convexity, the Hodlder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.

引用

页码：340 / 358

页数：19

共 29 条

[1] THE FLAW IN THE CONFORMABLE CALCULUS: IT IS CONFORMABLE BECAUSE IT IS NOT FRACTIONAL [J].

Abdelhakim, Ahmed A. .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2019, 22 (02) :242-254

[2] On conformable fractional calculus [J].

Abdeljawad, Thabet .

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

[3]

Anastassiou G.A., 2021, Generalized Fractional Calculus

[4] An efficient numerical technique for a biological population model of fractional order [J].

Attia, Nourhane ;

Akgul, Ali ;

Seba, Djamila ;

Nour, Abdelkader .

CHAOS SOLITONS & FRACTALS, 2020, 141

[5] Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative Is P-Convex [J].

Barani, A. ;

Barani, S. ;

Dragomir, S. S. .

JOURNAL OF APPLIED MATHEMATICS, 2012,

[6] On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals [J].

Budak, Huseyin ;

Hezenci, Fatih ;

Kara, Hasan .

ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)

[7] Hermite-Hadamard Type Inequalities for Twice Differantiable Functions via Generalized Fractional Integrals [J].

Budak, Huseyin ;

Ertugral, Fatma ;

Pehlivan, Ebru .

FILOMAT, 2019, 33 (15) :4967-4979

[8] Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula [J].

Dragomir, SS ;

Agarwal, RP .

APPLIED MATHEMATICS LETTERS, 1998, 11 (05) :91-95

[9]

Gabr A., 2021, Int. J. Appl. Comput. Math, V7, DOI [10.1007/s40819-021-01160-w, DOI 10.1007/S40819-021-01160-W]

[10]

Hezenci F., 2022, CUMHUR SCI J, V43, P477, DOI DOI 10.17776/csj.1088703

← 1 2 3 →