Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms

Jehad Alzabut, James Viji, Velu Muthulakshmi and Weerawat Sudsutad
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Jehad Alzabut: Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
James Viji: Department of Mathematics, Periyar University, Salem 636 011, Tamilnadu, India
Velu Muthulakshmi: Department of Mathematics, Periyar University, Salem 636 011, Tamilnadu, India
Weerawat Sudsutad: Department of General Education, Navamindradhiraj University, Bangkok 10300, Thailand

Mathematics, 2020, vol. 8, issue 6, 1-18

Abstract: In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.

Keywords: generalized proportional fractional operator; oscillation criteria; nonoscillatory behavior; damping and forcing terms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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