A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line

Abstract

In this article, we propose a coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line and study its existence result by using Schauder’s fixed point theorem. An example is provided to illustrate the results.

Existence and multiplicity of positive solutions to a system of fractional difference equations with parameters

“…Basic definitions and properties of fractional difference calculus were presented in [4], and discrete fractional boundary value problems have been found in . However, the studies of a system of fractional boundary value problems are quite rare (see [34][35][36][37][38][39][40][41][42]).…”

On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation

“…And the existing results of positive solutions for boundary value problem of nonlinear fractional difference equations is the hot spot which has been discussed in recent years. So, a large number of scholars have devoted themselves to the study of fractional difference equations, such as [1][2][3][4][5][6][7][8][9].…”

New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator

“…Absolute errors at the last mesh point over[0,1] with ν = 1 × 10 −3 3.0573 × 10 −4 3.0540 × 10 −5 0.004 2 5.0191 × 10 −3 4.8874 × 10 −4 4.8518 × 10 −5 × 10 −2 1.9220 × 10−3 1.9223 × 10 −4 0.008 Absolute errors at the last mesh point over [0, 1] with ν = Absolute errors at the last mesh point over [0, 1] with ν = × 10 −3 7.3613 × 10 −4 7.3580 × 10 −5 0.006 2 8.9548 × 10 −4 8.0795 × 10 −5 7.7668 × 10 −6 0.007 3 7.4921 × 10 −4 6.7530 × 10 −5 6.6793 × 10 −6 0.007 4 6.9383 × 10 −2 6.9755 × 10 −3 6.9792 × 10 −4 0.006 5 1.2357 × 10 −2 1.2451 × 10 −3 1.2460 × 10 −4 0.006 Absolute errors at the last mesh point over [0, 1] with ν = × 10 −3 1.9945 × 10 −4 1.9918 × 10 −5 0.007 2 5.3955 × 10 −3 5.2689 × 10 −4 5.2382 × 10 −5 0.007 3 6.0877 × 10 −3 6.1385 × 10 −4 6.1436 × 10 −5 0.005 4 7.5564 × 10 −2 7.5842 × 10 −3 7.5870 × 10 −4 0.005 5 2.0529 × 10 −2 2.0530 × 10 −3 2.0530 × 10 −4 0.006 Absolute errors at the last mesh point over [0, 1] with ν = 0.999. × 10 −16 8.8818 × 10 −16 1.3323 × 10 −15…”