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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.

MSC:

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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