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

Abstract

In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p,q)-integral that are used in our study.

On Solvability of Fractional (p,q)-Difference Equations with (p,q)-Difference Anti-Periodic Boundary Conditions

“…The authors in [13] obtained some existence results for impulsive quantum (p, q)-difference equations. In [14], some existence results for a boundary value problem of (p, q)-integrodifference equations with nonlocal fractional (p, q)-integral boundary conditions were presented. The existence of multiple positive solutions for a fractional (p, q)-difference equation under (p, q)-integral boundary conditions was discussed in [15].…”