Some modifications in conformable fractional integral inequalities

被引：25

作者：

Baleanu, Dumitru ^{[1
,2
,3
]}

Mohammed, Pshtiwan Othman ^{[4
]}

Vivas-Cortez, Miguel ^{[5
]}

Rangel-Oliveros, Yenny ^{[5
]}

机构：

[1] Inst Space Sci, MG-23, R-76900 Magurele, Romania

[2] Cankaya Univ, Dept Math, Ankara, Turkey

[3] China Med Univ, Dept Med Res, China Med Univ Hosp, Taichung, Taiwan

[4] Univ Sulaimani, Coll Educ, Dept Math, Sulaimani, Kurdistan Regio, Iraq

[5] Pontificia Univ Catolica Ecuador, Fac Ciencias Exactas & Nat, Escuela Ciencias Fis & Matemat, Quito, Ecuador

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Integral inequality; Conformable operator; Convex functions;

D O I：

10.1186/s13662-020-02837-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The prevalence of the use of integral inequalities has dramatically influenced the evolution of mathematical analysis. The use of these useful tools leads to faster advances in the presentation of fractional calculus. This article investigates the Hermite-Hadamard integral inequalities via the notion of F-convexity. After that, we introduce the notion of F-mu-convexity in the context of conformable operators. In view of this, we establish some Hermite-Hadamard integral inequalities (both trapezoidal and midpoint types) and some special case of those inequalities as well. Finally, we present some examples on special means of real numbers. Furthermore, we offer three plot illustrations to clarify the results.

引用

页数：25

共 54 条

[1]

Abdeljawad T., 2020, J FUNCT SPACES, V2020

[2] A generalized Lyapunov-type inequality in the frame of conformable derivatives [J].

Abdeljawad, Thabet ;

Alzabut, Jehad ;

Jarad, Fahd .

ADVANCES IN DIFFERENCE EQUATIONS, 2017,

[3] On conformable fractional calculus [J].

Abdeljawad, Thabet .

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

[4] Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions [J].

Abu Arqub, Omar ;

Al-Smadi, Mohammed .

SOFT COMPUTING, 2020, 24 (16) :12501-12522

[5] Application of Residual Power Series Method for the Solution of Time-fractional Schrodinger Equations in One-dimensional Space [J].

Abu Arqub, Omar .

FUNDAMENTA INFORMATICAE, 2019, 166 (02) :87-110

[6] Serum Adipokines as Predictors for the Outcome of Prostate Biopsies at Early Stage Prostate Cancer Diagnosis [J].

Ahmad, Ardalan E. ;

Mohammed, Aza ;

Bhindi, Bimal ;

Richard, Patrick O. ;

Fadaak, Kamel ;

Leao, Ricardo ;

Finelli, Antonio ;

Fleshner, Neil E. ;

Kulkarni, Girish S. .

CANCER MANAGEMENT AND RESEARCH, 2019, 11 :10043-10050

[7]

Al-Rifae M., 2017, COMPLEXITY, V2017

[8] Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means [J].

Alomari, M. ;

Darus, M. ;

Kirmaci, U. S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (01) :225-232

[9]

[Anonymous], 1965, J. SIAM Control, Ser. A

[10] New properties of conformable derivative [J].

Atangana, Abdon ;

Baleanu, Dumitru ;

Alsaedi, Ahmed .

OPEN MATHEMATICS, 2015, 13 :889-898

← 1 2 3 4 5 6 →