Some fractional integrals inequalities for h-preinvex functions and applications to numerical integration

An identity with parameters is constructed via Riemann-Liouville fractional integrals. With that, we derive some fractional integrals inequalities with parameters for h-preinvex functions. The "midpoint type", "trapezoidal type" and "Simpson type" integral inequalities...

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Published inZhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 49; no. 3; pp. 308 - 315
Main Authors Sun, Wenbing, Xie, Wenping
Format Journal Article
LanguageChinese
Published Hangzhou Zhejiang University 01.05.2022
Zhejiang University Press
Subjects
Fractional calculus
h-预不变凸函数
hermite-hadamard型不等式
Inequalities
Integrals
Numerical integration
Parameters
riemann-liouville分数阶积分
simpson型不等式
误差估计
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ISSN1008-9497
DOI10.3785/j.issn.1008-9497.2022.03.007

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Summary:An identity with parameters is constructed via Riemann-Liouville fractional integrals. With that, we derive some fractional integrals inequalities with parameters for h-preinvex functions. The "midpoint type", "trapezoidal type" and "Simpson type" integral inequalities are obtained respectively when the parameters are given special values. Finally,the error estimates of numerical integration are proposed to illustrate the applications of the results.
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ISSN:1008-9497
DOI:10.3785/j.issn.1008-9497.2022.03.007