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Zbl 0723.45002
Ross, Bertram; Sachdeva, Baldev K.
The solution of certain integral equations by means of operators of arbitrary order.
(English)
[J] Am. Math. Mon. 97, No.6, 498-503 (1990). ISSN 0002-9890

The authors study a Volterra integral equation of the second kind, $f(x)+1/\Gamma (\nu)\int\sp{x}\sb{0}(x-t)\sp{\nu -1}f(t)dt=g(x),$ involving a fractional order derivative or integral. This equation is solved by means of an operational calculus for fractional order integral and differential operators, and the result is compared to the result that one gets by using Laplace transforms.
[O.Staffans (Espoo)]
MSC 2000:
*45D05 Volterra integral equations
26A33 Fractional derivatives and integrals (real functions)

Keywords: Volterra integral equation of the second kind; fractional order derivative or integral; operational calculus for fractional order integral and differential operators; Laplace transforms

Cited in: Zbl 0838.34077

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