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

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.