Oscillatory Criteria of Nonlinear Higher Order $\Psi$-Hilfer Fractional Differential Equations

Abstract

In this paper, we study the forced oscillatory theory for higher order fractional differential equations with damping term via $\Psi$-Hilfer fractional derivative. We get sufficient conditions which ensure the oscillation of all solutions and give an illustrative example for our results. The $\Psi$-Hilfer fractional derivative according to the choice of the $\Psi$ function is a generalization of the different fractional derivatives defined earlier. The results obtained in this paper are a generalization of the known results in the literature, and present new results for some fractional derivatives.