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This paper provides the existence and representation of solution to aninitial value problem for the general multi-term linear fractional differentialequation with generalized Riemann-Liouville fractional derivatives and constantcoefficients by using operational calculus of Mikusinski's type. We prove thatthe initial value problem has the solution of if and only if some initialvalues should be zero.

Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms