On the fractional differential equations
In this paper we are concerned with the semilinear differential equation d^@ax(t)dt^@a=f(t,x(t)), t>;0 where @a is any positive real number. In [3] the author has proved the existence, uniqueness, and some properties of the solution of this equation when 0<@a<1. Here we mainly study (besides the other properties) the continuation of the solution of this equation to the solution of the corresponding initial value problem when [@a]=k, k=1,2,3,... Applications of singular integro-differential equations are considered.