Some trapezoid and midpoint type inequalities via fractional \((p,q)\) -calculus

Advances in Difference Equations

article

Neang, Pheak¹  Nonlaopon, Kamsing¹  Tariboon, Jessada²  Ntouyas, Sotiris K.³  Agarwal, Praveen⁵ 

[1] Department of Mathematics, Khon Kaen University;Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok;Department of Mathematics, University of Ioannina;Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University;International Center for Basic and Applied Sciences;Department of Mathematics, Anand International College of Engineering

关键词: Trapezoid type inequalities;    Midpoint type inequalities;    Quantum calculus;    q -shifting operator;    \((p;    q)\) -calculus;    Fractional \((p;    q)\) -integral;    Fractional \((p;    q)\) -integral inequalities;   

DOI  :  10.1186/s13662-021-03487-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q-trapezoid and q-midpoint type inequalities. Fractional$(p,q)$ -calculus on finite intervals, particularly the fractional$(p,q)$ -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional$(p,q)$ -integral on finite intervals. Then, the obtained results are used to derive some fractional$(p,q)$ -trapezoid and$(p,q)$ -midpoint type inequalities.

【 授权许可】

CC BY