Sufficient conditions for oscillation of a nonlinear fractional nabla difference system

Abstract

In this paper, we study the oscillation of nonlinear fractional nabla difference equations of the form where c and α are constants, is the Riemann–Liouville fractional nabla difference operator of order is a real number, and . Some sufficient conditions for oscillation are established.

A Survey on the Oscillation of Solutions for Fractional Difference Equations

“…Motivated by the paper [38], the authors [42] investigated the oscillation of a nonlinear fractional nabla difference system of the form:…”

The Asymptotic Behavior of Solutions for a Class of Nonlinear Fractional Difference Equations with Damping Term

“…Assume that ( ) is an eventually positive solution of (6); then we obtain that ( ) ( )[Δ( ( )Δ ( ))] is strictly decreasing on [ 1 , ∞); by (27) we have,…”

“…However, as we all know, it is usually difficult to find the exact solutions to fractional differential or difference equations. In recent years, the study on qualitative properties of solutions of fractional differential equations, such as the existence, uniqueness, boundedness, oscillation, and other asymptotic behaviors, attracted much attention and some excellent results were obtained; we refer the reader to see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] and the references cited therein.…”

Optimal solutions for singular linear systems of Caputo fractional differential equations

“…In the last decade, many authors have studied problems of fractional differential-difference equations and have derived interesting results on different type of problems for given initial or boundary conditions; see other studies. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] Focus has also been given in the mathematical modelling of many phenomena by using fractional operators. The theory of fractional differential equations (FDEs) is a promising tool for applications in physics, electrical engineering, control theory, and in applications where the memory effect appears; see other studies.…”