Partial fractional derivatives of Riesz type and nonlinear fractional differential equationsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 27 ноября 2016 г.
Аннотация:Generalization of fractional derivatives of non-integer orders for N-dimensional Euclidean space are proposed. These fractional derivatives of the Riesz type can be considered as partial derivatives of non-integer orders. In contrast to the usual Riesz derivatives, the suggested derivatives give the usual partial derivatives for integer values of orders. For integer values of orders the partial fractional derivatives of the Riesz type are equal to the standard partial derivatives of integer orders with respect to coordinate. Fractional generalizations of the nonlinear equations such as sine-Gordon, Boussinesq, Burgers, Korteweg-de Vries and Monge-Ampere equations for nonlocal continuum are considered.