Oscillation For Fractional Delay Differential Equations And Partial Differential Equations

Oscillation theory of functional di?erential equations and partial di?erentialequations with integer derivative has been developed rapidly in the past decade,and a lot of theories has been obtained. Though fractional di?erential equationshave gained more development, there is not enough theories comparison withthe integer order, even not be started. To the best of our knowledge, nothinghas been done with oscillations of fractional functional di?erential equations andpartial di?erential equations.In this paper, we discuss the theorem of oscillation for fractional delay di?er-ential equations and partial di?erential equations. In Chapter 2, we present theoscillation for the fractional delay di?erential equations with Riemann-Liouvillefractional derivative, su?cient conditions and some corollaries for all solutionsof fractional delay di?erential equations to be oscillatory are obtained by usingthe Laplace transforms. In chapter 3, we survey the oscillation for the frac-tional partial di?erential equations with Riemann-Liouville fractional derivative,in addition with the chapter 2, su?cient conditions and some corollaries for allsolutions of fractional partial di?erential equations to be oscillatory are obtainedby using the Laplace transforms and Green's formula.