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.
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.
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
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
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