On the Cauchy problem for some fractional order partial differential equations

In the present paper, we study the Cauchy problem for a fractional order partial differential equation of the form where 0<α 1 and ∑q=2maq(x,t)Dxq is a uniformly elliptic partial differential operator. The existence and uniqueness of the solution of the considered Cauchy problem is studied, also a continuity property is considered.