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

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