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Numerical schemes for integro-differential equations with Erdélyi-Kober fractional operator. (English) Zbl 1422.65456
The paper discusses numerical schemes for discretising the fractional differential operator of Erdélyi-Kober type which arise when self-similar solutions are considered for sub-diffusive evolution equations. The authors consider how the E-Y operator can be discretised, using a range of simple methods. Then they consider how finite difference methods can be applied to an integro-differential equation with E-K operator. They derive the truncation error and give a convergence theorem that are confirmed in an example.

MSC:
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
34A08 Fractional ordinary differential equations and fractional differential inclusions
34K37 Functional-differential equations with fractional derivatives
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