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.
Highlights
The ordinary calculus of Newton and Leibniz is well known to be investigated extensively and intensively to produce a large number of related formulas and properties as well as applications in a variety of fields ranging from natural sciences to social sciences
In the early eighteenth century, the well-known mathematician Leonhard Euler (1707–1783) established quantum calculus or q-calculus, which is the study of calculus without limits, in the way of Newton’s work for infinite series
Many physical and mathematical problems have led to the necessity of studying qcalculus; for instance, Fock [3] studied the symmetry of hydrogen atoms using the qdifference equation
Summary
The ordinary calculus of Newton and Leibniz is well known to be investigated extensively and intensively to produce a large number of related formulas and properties as well as applications in a variety of fields ranging from natural sciences to social sciences. Theorem 2.2 ([72]) If f , g : [a, b] → R are continuous functions and λ ∈ R, the following formulas hold: (i) adp,q s
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