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 study an initial–boundary value problem for a fractional parabolic equation on a metric star graph in Sobolev spaces. We start by proving existence and uniqueness results for strong solutions by the classical functional method based on a priori estimates. Moreover, the present paper is the first to consider an inverse source problem with an integral overdetermination condition for space-time fractional derivatives in Sobolev spaces. Transforming the inverse problem into an operator-based equation, we show that the corresponding resolvent operator is well defined.