Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-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.

Keywords

• fractional (<i>p</i>,<i>q</i>)-integral
• fractional (<i>p</i>,<i>q</i>)-difference
• nonlocal boundary value problems
• existence