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In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergence, efficiency and simplicity of the method. Mathematics Subject Classification: 45J05, 65T60fatcat:fjquslglkjadvioafle5bablpi