Oscillation for a Class of Fractional Differential Equation

Abstract

We consider the oscillation for a class of fractional differential equation[r(t)g(D-αy)(t)]'-p(t)f∫t∞‍(s-t)-αy(s)ds=0,fort>0,where0<α<1is a real number andD-αyis the Liouville right-sided fractional derivative of orderαofy. By generalized Riccati transformation technique, oscillation criteria for a class of nonlinear fractional differential equation are obtained.

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

“…Using hypothesis and Lemma 3.3, we have from (16) (15) implies that the last inequality has no eventually positive solution, a contradiction. This completes the proof.…”

“…Several papers concerning neutral parabolic differential equations have appeared recently (for example see [7] [8]). The oscillatory theory of solutions of fractional differential equations has received a great deal of attention [9]- [15].…”

Oscillation Criteria for a Class of Discrete Nonlinear Fractional Equations

“…We proceed as in the proof of Theorem (3.4) to get (10). Multiplying (10) by H(t, s) and summing from t 1 to t 1, we obtain (12) Using summation by parts formula, we get Letting t, we have which is a contradiction to (11). The proof is complete.…”

“…Fractional differential equations are generalizations of classical differential equations of integer order. In recent days, oscillatory behavior of fractional differential/difference equations has been investigated by authors, see papers [2]- [12]. Formal treatment on the subject of fractional derivatives and fractional integrals are presented in the books, see [16]- [19].…”

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].…”