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In view of the usefulness and importance of the fractional differential equations in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional differential equation and Volterra type differintegral equation. The solutions are obtained in a straightforward manner by the application of Riemann-Liouville fractional integral operator and its interesting properties. As applications of the main results, solutions of certain generalized fractional kinetic equations involving generalized Mittag-Leffler function are also studied. Moreover, results for some particular values of the parameters are also pointed out.