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Browsing by Author "Nigmatullin, Raoul"

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    Article
    Citation - WoS: 8
    Citation - Scopus: 8
    Balance equations with generalised memory and the emerging fractional kernels
    (Springer, 2021) Nigmatullin, Raoul; Baleanu, Dumitru; Baleanu, Dumitru; Fernandez, Arran; 56389; Matematik
    In this paper, we consider the mechanism of a memory effect based on linear or nonlinear systems of balance equations. By considering a chain of balance equations, connecting each particle to the next by means of a memory kernel, it becomes possible to derive generalised expressions for the overall memory kernel that connects the initial particle to the last particle. We consider several different cases and types of systems, both linear and nonlinear. By assuming a general type of fractional integral operator to describe each balance equation, we derive an expression for the generalised memory which yields a more general type of fractional integral operator based on multivariate series. Some cases of this, such as multivariate Mittag-Leffler-type functions, are already known in mathematics, but they have never discovered real applications until now.
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    Article
    Citation - WoS: 62
    Citation - Scopus: 69
    Fractional Newtonian mechanics
    (de Gruyter Poland Sp Z O O, 2010) Baleanu, Dumitru; Baleanu, Dumitru; Golmankhaneh, Alireza K.; Nigmatullin, Raoul; Golmankhaneh, Ali K.; Matematik
    In the present paper, we have introduced the generalized Newtonian law and fractional Langevin equation. We have derived potentials corresponding to different kinds of forces involving both the right and the left fractional derivatives. Illustrative examples have worked out to explain the formalism.