On the Second-Order Quantum (p,q)-Difference Equations with Separated Boundary Conditions

Abstract

In this paper, we investigate the existence and uniqueness of solutions for a boundary value problem for second-order quantum (p,q)-difference equations with separated boundary conditions, by using classical fixed point theorems. Examples illustrating the main results are also presented.

Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions

“…The subject of (p, q)-calculus is known as the extension of q-calculus to its twoparameter (p, q) variant and has efficient applications in many fields. One can find some useful information about the (p, q)-calculus in [22][23][24][25][26][27][28][29][30].…”

Separate Fractional (p,q)-Integrodifference Equations via Nonlocal Fractional (p,q)-Integral Boundary Conditions

“…In the literature, there exist few papers studying boundary value problems for (p, q)-difference equations, because the (p, q)-fractional operator has been introduced recently. In [18], the following (p, q) boundary value problem for second order (p, q)-difference equations with separated boundary conditions was studied:…”

On fractional $(p,q)$-calculus

“…For some results on the study of (p, q)calculus, we refer to [27][28][29][30][31][32][33][34][35][36][37][38]. For example, Sadjang [30] investigated the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulas; the boundary value problems for (p, q)-difference equations were initiated in [35,36]; and we see the concept of (p, q)-Beta and (p, q)-gamma functions in [37,38]. We can see the applications of (p, q)calculus in [39][40][41][42][43][44].…”