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This article is cited in 18 scientific papers (total in 18 papers)
Differentical equations, dynamical systems and optimal control
Fractional diffusion equation with discretely distributed differentiation operator
A. V. Pskhu Institute of Applied Mathematics and Automation, Shortanova street, 9A,
360000, Nalchik, Russia
Abstract:
We discuss an initial value problem for a fractional diffusion equation with discretely distributed fractional differentiation operator with respect to time variable. We construct a fundamental solution of the considered equation, give a solution of the problem under study, and prove a uniqueness theorem in the class of rapid growth functions. The fractional differentiation is given by the Dzhrbashyan–Nersesyan operator, and the corresponding results for equations with Caputo and Riemann–Liouville derivatives are particular cases of proved assertions.
Keywords:
fractional diffusion equation, Cauchy problem, fractional derivative, discretely distributed fractional differentiation operator, multi-term fractional diffusion equation, Dzhrbashyan–Nersesyan fractional differentiation operator, Riemann–Liouville derivative, Caputo derivative, Tychonoff condition, Wright function.
Received July 17, 2016, published December 14, 2016
Citation:
A. V. Pskhu, “Fractional diffusion equation with discretely distributed differentiation operator”, Sib. Èlektron. Mat. Izv., 13 (2016), 1078–1098
Linking options:
https://www.mathnet.ru/eng/semr736 https://www.mathnet.ru/eng/semr/v13/p1078
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Abstract page: | 438 | Full-text PDF : | 166 | References: | 49 |
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