PHILOS-TYPE OSCILLATION CRITERIA FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSIVE CONDITIONS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 |
The present article is concerned with the oscillatory nature of the fractional differential equation of order $\alpha \in (2,3)$ with impulsive effects. By employing a generalized Riccati transformation, we derive several oscillation criteria of Philos type, which are either new or improve several recent results in the literature. Also, we show the stability of the considered problem. To obtain the results, we transform the fractional differential equation into a second-order ordinary differential equation. In addition, we provide examples to show the effectiveness of the results.
Keywords and Phrases
Fractional differential equations, Impulsive conditions, Oscillation, Differential inequality method.
A.M.S. subject classiﬁcation
26A33, 34A08, 34D20, 34K11, 35R12.