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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.

Reviewer: H.M.Srivastava (Victoria)

### MSC:

44A45 | Classical operational calculus |

26A33 | Fractional derivatives and integrals |

34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |

### Keywords:

hyper-Bessel differential operator; Erdélyi-Kober fractional derivatives; fractional calculus; linear operator; Weierstrass approximation theorem; convolution quotients; operational calculus; Riemann-Liouville fractional differential operator; Cauchy boundary-value problem
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\textit{Yu. F. Luchko} and \textit{H. M. Srivastava}, Comput. Math. Appl. 29, No. 8, 73--85 (1995; Zbl 0824.44011)

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### References:

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