The exact solution of certain differential equations of fractional order by using operational calculus

In the present paper, the authors first develop an operational calculus for the familiar Riemann-Liouville fractional differential operator. This operational calculus is then used here to solve a Cauchy boundary-value problem for a certain linear equation involving the Riemann-Liouville fractional derivatives. Relevant connections are also indicated with the special cases of the equation, which were solved earlier by using other methods.