Oscillation of fractional order functional differential equations with nonlinear damping

Abstract

Abstract:In this paper, we are concerned with the oscillatory behavior of a class of fractional di erential equations with functional terms. The fractional derivative is de ned in the sense of the modi ed Riemann-Liouville derivative. Based on a certain variable transformation, by using a generalized Riccati transformation, generalized Philos type kernels, and averaging techniques we establish new interval oscillation criteria. Illustrative examples are also given.

Note on the fractional Mittag-Leffler functions by applying the modified Riemann-Liouville derivatives

“…The most useful alternative which has been proposed to cope with this feature is known Caputo derivative [6], but in this derivative fractional derivative would be defined for differentiable functions only. A modification of the Riemann-Liouville has been defined to deal with non-differentiable functions [3,4,9,21,16,23] and it is given as: Definition 1.1. Let f : R −→ R, x −→ f (x) denote a continuous function.…”

Kesirli Mertebeden Doğrusal Olmayan Diferensiyel Denklemlerin Salınımlılığı Üzerine

“…Research on oscillation of various equations like ordinary and partial differential equations, difference equations, dynamic equations on time scales and fractional differential equations has been a hot topic in the literature, and much effort has been made to establish new oscillation criteria for these equations [14][15][16][17][18][19][20][21][22][23][24]. In these investigations, we notice that very little attention is paid to oscillation of fractional differential equations [25][26][27][28][29][30][31].…”