# Riccati technique for oscillation of half-linear/Emden-Fowler neutral dynamic equations

Volume 29, Issue 4, pp 387--398
Publication Date: November 24, 2022 Submission Date: December 24, 2021 Revision Date: January 20, 2022 Accteptance Date: May 24, 2022
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### Authors

S. H. Saker - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt. - Department of Mathematics, Faculty of Science, New Mansoura University, New Mansoura City, Egypt. A. K. Sethi - Department of Mathematics, Sambalpur University, Sambalpur-768019, India. O. Tunc - Department of Computer, Baskale Vocational School, Van Yuzuncu Yi l University, 65080 Campus, Van, Turkiye. J. Alzabut - Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia. - Department of Industrial Engineering, OSTIM Technical University, Ankara 06374, Turkiye.

### Abstract

By using the Riccati technique, which reduces the higher order dynamic equations to a Riccati dynamic inequality, we will establish some new sufficient conditions for the oscillation of half-linear/Emden-Fowler neutral dynamic equation of the form $(r(\varrho)((\mathbf{\mathbf{x}}(\varrho)+p(\varrho)\mathbf{x}(\tau (\varrho)))^{\Delta })^{\gamma })^{\Delta }+q(\varrho)\mathbf{x}^{a }(\delta (\varrho))+v(\varrho)\mathbf{x}^{\beta }(\eta (\varrho))=0,$ on a time scale $\mathcal{T}$, where $\gamma$, $a$, and $\beta$ are quotients of odd positive integers. An example with particular equation is constructed in consistent to the above equation and oscillation criteria are established for its solution.

### Share and Cite

##### ISRP Style

S. H. Saker, A. K. Sethi, O. Tunc, J. Alzabut, Riccati technique for oscillation of half-linear/Emden-Fowler neutral dynamic equations, Journal of Mathematics and Computer Science, 29 (2023), no. 4, 387--398

##### AMA Style

Saker S. H., Sethi A. K., Tunc O., Alzabut J., Riccati technique for oscillation of half-linear/Emden-Fowler neutral dynamic equations. J Math Comput SCI-JM. (2023); 29(4):387--398

##### Chicago/Turabian Style

Saker, S. H., Sethi, A. K., Tunc, O., Alzabut, J.. "Riccati technique for oscillation of half-linear/Emden-Fowler neutral dynamic equations." Journal of Mathematics and Computer Science, 29, no. 4 (2023): 387--398

### Keywords

• Oscillation
• nonoscillation
• half-linear/Emden-Fowler neutral dynamic equation
• time scales

•  34C10
•  34K11
•  39A21
•  34A40
•  34N05