The exact solution of certain differential equations of fractional order by using operational calculus. (English) Zbl 0824.44011

First the authors develop an operational calculus for the familiar Riemann-Liouville fractional differential operator. This operational calculus is then used 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.


44A45 Classical operational calculus
26A33 Fractional derivatives and integrals
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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