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Balance equations with generalised memory and the emerging fractional kernels

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Date

2021

Authors

Nigmatullin, Raoul
Baleanu, Dumitru
Fernandez, Arran

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Abstract

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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Nonlinear Systems, Balance Equations, Memory Kernels, Fractional Integrals

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Citation

Nigmatullin, Raoul; Baleanu, Dumitru; Fernandez, Arran (2021). "Balance equations with generalised memory and the emerging fractional kernels", Nonlinear Dynamics, Vol. 104, no. 4, pp. 4149-4161.

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Nonlinear Dynamics

Volume

104

Issue

4

Start Page

4149

End Page

4161