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The solution of certain integral equations by means of operators of arbitrary order. (English) Zbl 0723.45002

The authors study a Volterra integral equation of the second kind, \(f(x)+1/\Gamma (\nu)\int^{x}_{0}(x-t)^{\nu -1}f(t)dt=g(x),\) 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.
Reviewer: O.Staffans (Espoo)

MSC:

45D05 Volterra integral equations
26A33 Fractional derivatives and integrals
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