Opuscula Math. 40, no. 5 (2020), 549-568
https://doi.org/10.7494/OpMath.2020.40.5.549
Opuscula Mathematica
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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- Said Rezk Grace
https://orcid.org/0000-0001-8783-5227
- Faculty of Engineering, Cairo University, Department of Engineering Mathematics, Giza 12221, Egypt
- Jehad Alzabut (corresponding author)
https://orcid.org/0000-0002-5262-1138
- Prince Sultan University, Department of Mathematics and General Sciences, 11586 Riyadh, Saudi Arabia
- Sakthivel Punitha
- Periyar University, Department of Mathematics, Salem-636 011, Tamilnadu, India
- Velu Muthulakshmi
https://orcid.org/0000-0003-0125-5032
- Periyar University, Department of Mathematics, Salem-636 011, Tamilnadu, India
- Hakan Adıgüzel
https://orcid.org/0000-0002-8948-806X
- Sakarya University of Applied Sciences, Vocational School of Arifiye, Arifiye 54580, Sakarya, Turkey
- Communicated by Josef Diblík.
- Received: 2020-01-11.
- Revised: 2020-08-20.
- Accepted: 2020-08-28.
- Published online: 2020-10-10.