A Nonlocal Initial Conditional Boundary Value Problem on Metric Graph

The main task of the present research is a nonlocal boundary value problem for a time-fractional differential equation involving the Hilfer fractional derivative on a metric star graph. The main goal of this work is to study the uniqueness and existence of a solution to the problem formulated. Using Fourier’s method, we find a solution to the investigated problem in the form of the Fourier series. The uniqueness of the solution is proved by using a priori estimates of the solution.