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Zbl 0824.44011
Luchko, Yu.F.; Srivastava, H.M.
The exact solution of certain differential equations of fractional order by using operational calculus. (English)
[J] Comput. Math. Appl. 29, No.8, 73-85 (1995). ISSN 0898-1221

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.
[H.M.Srivastava (Victoria)]

MSC 2000:: *44A45 Classical operational calculus
26A33 Fractional derivatives and integrals (real functions)
34A25 Analytical theory of ODE

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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