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Overview to mathematical analysis for fractional diffusion equations – new mathematical aspects motivated by industrial collaboration. (English) Zbl 1206.35247

Summary: The mathematics turns out to be useful for creation of innovations in the industry, and the mathematical knowledge and thinking manners are used effectively for that purpose. However, this is only one aspect of the industrial mathematics where various existing mathematical knowledge are applied for solving required subjects from industry. On the other hand, one can see the opposite direction; Pursuit of industrial purposes inspires to create new fields of mathematics by motivating and activating existing researches. This is an important aspect of the industrial mathematics because it does not only give tools for solving concrete problems, but also enriches the existing branches of mathematics. In this article, as such a possible example, we discuss a fractional diffusion equation which has been studied already comprehensively from the theoretical interests, but the researches are expanded as a mathematical topic in view of the industrial applications.

MSC:

35R11 Fractional partial differential equations
34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
76R50 Diffusion
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