American Review of Mathematics and Statistics

On the Oscillation of Solutions of Fractional Vector Partial Differential Equations with Deviating Arguments
V. Sadhasivam, J. Kavitha

Abstract
In this article, we investigate the oscillation of solutions of a class of fractional vector partial differential equations with deviating arguments of the form ? ( ) ( , )?= ( ) ( , ) ( ) ( , ( )) =1 D , r t D , U x t a t U x t ai t U x i t m i t t ? ? ? ? ?? ? ? ? ( , ) ( ) ( , ( )) ( , ( )) =1 0 p x t f t s U x j s ds U x j t t j j k j ? ? ? ? ? ? ?? ? ? ? ? ? ? ?F(x,t), (x,t)?G = ?? R? , subject to the boundary condition ? ( , ) ( , ) = 0, ( , )???? ?. ? ? U ? x t U x t x t R ? We will establish the sufficient conditions for H-oscillation of solutions of given system, where H is a unit vector in Rn , n ? 1. We also provide an example to illustrate the main results.

Full Text: PDF     DOI: 10.15640/arms.v5n1a5