Cauchy Problem for Subdiffusion Equation on Metric Star Graph with Edge Dependent Order of Time-Fractional Derivative

This work is devoted to study the Cauchy problem for subdiffusion equation on the metric star graph with edge-dependent order of time-fractional derivatives. Using the method of potential the problem is reduced to the generalized Abel’s integral equation. The analytical solution of the integral equation is founded. Uniqueness of the solution is proved by the method of energy integrals.

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