SIMPSON-LIKE INEQUALITIES FOR TWICE DIFFERENTIABLE (s,P)-CONVEX MAPPINGS INVOLVING WITH AB-FRACTIONAL INTEGRALS AND THEIR APPLICATIONS

被引：11

作者：

Yuan, Xiaoman ^{[1
]}

Xu, Lei ^{[1
]}

Du, Tingsong ^{[1
,2
]}

机构：

[1] China Three Gorges Univ, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China

[2] China Three Gorges Univ, Coll Sci, Dept Math, Yichang 443002, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2023年 / 31卷 / 03期

关键词：

Simpson-type Integral Inequalities; (s; P)-convex Mappings; AB-fractional Integrals; CONVEX-FUNCTIONS; OPERATORS;

D O I：

10.1142/S0218348X2350024X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

First, we establish the parametrized integral identity and its improved version via Atangana-Baleanu (AB) fractional integrals. For the focus of this paper, we utilize the resulting identities to derive a series of Simpson-like integral inequalities for mappings whose second-order derivatives belong to the (s,P)-convexity and (s,P)-concavity in absolute value. And a couple of outcomes, concerning the Simpson-like quadrature formulas, the q-digamma functions and the modified Bessel functions, are introduced as applications separately in the end.

引用

页数：31

共 48 条

[1] Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel [J].

Abdeljawad, Thabet ;

Baleanu, Dumitru .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (03) :1098-1107

[2] Refinements of Ostrowski Type Integral Inequalities Involving Atangana-Baleanu Fractional Integral Operator [J].

Ahmad, Hijaz ;

Tariq, Muhammad ;

Sahoo, Soubhagya Kumar ;

Askar, Sameh ;

Abouelregal, Ahmed E. ;

Khedher, Khaled Mohamed .

SYMMETRY-BASEL, 2021, 13 (11)

[3] Fractional Integral Inequalities via Atangana-Baleanu Operators for Convex and Concave Functions [J].

Akdemir, Ahmet Ocak ;

Karaoglan, Ali ;

Ragusa, Maria Alessandra ;

Set, Erhan .

JOURNAL OF FUNCTION SPACES, 2021, 2021

[4] Some New Simpson's-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators [J].

Ali, Muhammad Aamir ;

Kara, Hasan ;

Tariboon, Jessada ;

Asawasamrit, Suphawat ;

Budak, Huseyin ;

Hezenci, Fatih .

SYMMETRY-BASEL, 2021, 13 (12)

[5] Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination? [J].

Atangana, Abdon .

CHAOS SOLITONS & FRACTALS, 2020, 136

[6] Modeling attractors of chaotic dynamical systems with fractal-fractional operators [J].

Atangana, Abdon ;

Qureshi, Sania .

CHAOS SOLITONS & FRACTALS, 2019, 123 :320-337

[7] NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory and Application to Heat Transfer Model [J].

Atangana, Abdon ;

Baleanu, Dumitru .

THERMAL SCIENCE, 2016, 20 (02) :763-769

[8] Some Generalized Fractional Integral Inequalities via Harmonic Convex Functions and Their Applications [J].

Awan, Muhammad Uzair ;

Akhtar, Nousheen ;

Raissouli, Mustapha ;

Kashuri, Artion ;

Javed, Muhammad Zakria ;

Noor, Muhammad Aslam .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2022, 2022

[9] SOME SIMPSON TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR FUNCTIONS OF BOUNDED VARIATION [J].

Bounoua, Mohamed Doubbi ;

Yin, Chuntao .

JOURNAL OF MATHEMATICAL INEQUALITIES, 2021, 15 (04) :1473-1486

[10] Some parameterized Simpson-, midpoint-and trapezoid-type inequalities for generalized fractional integrals [J].

Budak, Huseyin ;

Yildirim, Seda Kilinc ;

Sarikaya, Mehmet Zeki ;

Yildirim, Huseyin .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2022, 2022 (01)

← 1 2 3 4 5 →