Fractional parabolic problems with a nonlocal initial condition

In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem

where is a bounded domain, the function a can be a singular potential, g is a suitable function which will be specified later and p, θ Abstract. In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem under natural conditions on the data. The question of global existence is also analyzed.