On the oscillation of fractional differential equations

Abstract

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the formwhere D q a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville differential operator is replaced by Caputo's differential operator.MSC 2010 : Primary 34A08: Secondary 34C10, 26A33

Forced Oscillation of Solutions of a Fractional Neutral Partial Functional Differential Equation

“…Assume that ( ) z t satisfies (11). Using hypothesis and Lemma 3.3, we have from (16) (15) implies that the last inequality has no eventually positive solution, a contradiction.…”

Oscillation of Solutions to Fractional Partial Differential Equations with Several Delays

“…In recent years, oscillatory behavior of solutions of fractional ordinary differential equations have been studied by authors [3][4][5][6][7][8][9][10][11]. However, there is a scarcity in the study of oscillation theory of fractional partial differential equations up to now, we refer to [12][13][14][15][16].…”

Oscillation criteria for a certain class of fractional order integro-diferential equations

“…To the best of our knowledge, the paper by Grace et al [15] has initiated the study of oscillation theory for fractional differential equations. In mentioned paper, the authors established several results criteria for solutions of equations in the form …”