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.

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