Initial value/boundary value problem for composite fractional relaxation equation

We consider initial value/boundary value problem for composite fractional relaxation equation involving Caputo fractional derivative of order 0<β<1. We prove by means of change of variable that this problem is reduced to initial value/boundary value problem for fractional diffusion equation involving Riemann-Liouville fractional derivative of order β=1-α. Then by means of eigenfunctions expansions, we establish the existence and uniqueness of solution.