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

Said Rezk Grace
Jehad Alzabut
Sakthivel Punitha
Velu Muthulakshmi
Hakan Adıgüzel

Abstract. 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 transformation 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.

Keywords: Caputo difference operator, nonoscillation criteria, fractional difference equation, mathematical inequalities.

Mathematics Subject Classification: 34A08, 39A21.

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