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On the nonoscillatory behavior of solutions of three classes of fractional difference equations

Grace Said Rezk, Alzabut Jehad, Punitha Sakthivel, Muthulakshmi Velu, Adiguzel Hakan

Opuscula Mathematica

2020

Vol. 40, no. 5

549--568

In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transfor mation technique, we employ herein an easily verifiable approach based on the fractional Taylor’s difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.