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.
Highlights
Quantum calculus or q-calculus is the modern name for the study of calculus without limits. q-calculus was first introduced by Jackson [1,2] in 1910
It contains nonlocal boundary conditions; it is well known that the study of nonlocal boundary value problems is of significance, since they have applications in physics and other areas of applied mathematics
An Existence Result we present an existence result for the boundary value problem (4) by using the Schaefer’s fixed-point theorem [24]
Summary
Quantum calculus or q-calculus is the modern name for the study of calculus without limits. q-calculus was first introduced by Jackson [1,2] in 1910. There exist few papers studying boundary value problems for (p, q)-difference equations, because the (p, q)-fractional operator has been introduced recently. Boundary value problems for fractional (p, q)integrodifference equations with Robin boundary conditions were studied in [23], where the authors established existence and uniqueness results for the following problem: Dαp,qu(t) = F t, u(t), Ψγp,qu(t), Dνp,qu(t) , t ∈ IpT,q, λ1u(η) + λ2Dpβ,qu(η) = φ1(u), η ∈ IpT,q −. We notice that the the boundary value problem (4) is of general type, concerning both (p, q)-fractional integral and (p, q)-fractional derivative operators It contains nonlocal boundary conditions; it is well known that the study of nonlocal boundary value problems is of significance, since they have applications in physics and other areas of applied mathematics. The papers ends with a section that illustrates the conclusions
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