Fractional-differential approach to describe the process of feeding metals and alloys solidifying under controlled gas pressure
DOI:
https://doi.org/10.34185/1562-9945-4-135-2021-15Keywords:
фільтрація, математична модель, дробна похідна, дрібно-диференційне рівняння, узагальнений закон ДарсіAbstract
To describe the processes of filtration in the folding dendritic-porous middle of the proponation, a number of fractional-differential mathematical models of the diffusion type. Described non-linear, how to take the shot of the abducted Riman-Leeuwill for an hour, as it can be stuck for a correct description of the single-phase filtration of not Newtonian age in the porous middle.
The two-phase zone, which is established during the transition from melting from hard to hard mill, can often be characterized by abnormal kinetics of resistance. The peculiarities of kinetics in the whole range of winners are related to the issues of widespread nonlocality, in a number of types, memory defects, which adhere to the progressive laws. The mathe-?atical apparatus, which allows to adequately describe such processes, is the theory of integration-differentiation of the fractional order.
Victorians in robotic thinking have a phenomenological character, so the possibility of their dependence in a specific, practical dermal condition is blamed on the basis of experimental results, so that the validity of other differences is confirmed. Stagnation of the given approach for describing the dynamics of the process of vitality of the two-phase zones and metals and alloys, which solidifies in the minds of a regulated gas vice. Presented in the fractional-differential robotic model of filtration are classified as abnormal diffusion. A characteristic feature of the ryvnyan, which is derived from different types of differential models of filtration, is not the same. With a whole model, they preserve the structure of the classical lines of filtration in the whole order and pass into them in boundary drops, if the order of the other differentiation is old.
Vivchennya yakіsnyh authorities otrimanih іvnyans, and also prompts їh numerical decisions є to finish nontrivial zavdannyi, as vimagayut in the skin okremomu vampad of independent thought.
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