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

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 22
• Main Authors: Neang, Pheak, Nonlaopon, Kamsing, Tariboon, Jessada, Ntouyas, Sotiris K., Agarwal, Praveen
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 13.07.2021; Springer Nature B.V; SpringerOpen
• Subjects: ( p , q ) $(p,q)$ -calculus; Analysis; Calculus; Continuity (mathematics); Difference and Functional Equations; Fractional ( p , q ) $(p,q)$ -integral; Fractional calculus; Functional Analysis; Identities; Inequalities; Integrals; Intervals; Mathematical analysis; Mathematics; Mathematics and Statistics; Midpoint type inequalities; Ordinary Differential Equations; Partial Differential Equations; q-shifting operator; Quantum calculus; Trapezoid type inequalities; Midpoint type inequalities; 05A30; 26D10; shifting operator; integral; 26A33; Fractional; integral inequalities; Trapezoid type inequalities; calculus; Quantum calculus; 26D15
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03487-6

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.