Fractional (p,q)-Calculus on Finite Intervals and Some Integral Inequalities

Abstract

Fractional q-calculus has been investigated and applied in a variety of fields in mathematical areas including fractional q-integral inequalities. In this paper, we study fractional (p,q)-calculus on finite intervals and give some basic properties. In particular, some fractional (p,q)-integral inequalities on finite intervals are proven.

Some (p, q)-Integral Inequalities of Hermite–Hadamard Inequalities for (p, q)-Differentiable Convex Functions

“…Recently, the concept of the (p, q) b -integral and (p, q) bderivative over finite intervals was proposed by Vivas-Cortez et al [29] in 2021. In the past few years, the topic of (p, q)-calculus has become interesting in various integral inequalities for many researchers, and the results of (p, q)-calculus can be found in [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], and the references cited therein.…”

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

“…In 2020, Kunt and Aljasem [40] proved Riemann-Liouville fractional q-trapezoid and q-midpoint type inequalities for convex functions. Furthermore, in 2021, Neang et al [41] introduced fractional (p, q)-calculus on finite intervals and proved some well-known integral inequalities.…”

Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order

“…Moreover, the definition of q-derivative and q-integral is studied and gradually developed by many researchers (see [11,23,24,28]). The definitions of q-derivative and q-integral are developed, which are based on the q-Riemann-Liouville fractional integral.…”