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Numerical solution of a linear system with a fractional power. (Russian. English summary) Zbl 1413.65287

Summary: We investigate numerical solutions of linear ordinary and partial differential equations. Cauchy’s problem for ordinary equations of first and second order are generalized with fractional power of finite operator. Condition of regularization for the difference operator analogue of a fractional power is represented.

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
34A08 Fractional ordinary differential equations

References:

[1] [1] V. E. Tarasov, Modeli teoreticheskoi fiziki s integro-differentsirovaniem drobnogo poryadka, RKhD, M.-Izhevsk, 2011, 568 pp.
[2] [2] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp. · Zbl 1066.26005
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