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

Abstract

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.