Inverse source problem for the space-time fractional parabolic equation on a metric star graph with an integral overdetermination condition

In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are proved with the classical functional method based on a priori estimates. Moreover, the inverse source problem with the integral overdetermination condition for space-time fractional derivatives in Sobolev spaces is first considered in the present paper. By transforming the inverse problem to the operator-based equation, we showed that the corresponding resolvent operator is well-defined.