Approximate construction of new conservative physical magnitudes through the fractional derivative of polynomial-type functions: A particular case in semiconductors of type AlxGa1¡xAs

Julio Cesar Campos García*, Carlos Figueroa Navarro, Martin Eduardo Molinar Tabares, L. Castro-A.

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The fractional calculus has a very large diversification as it relates to applications from physical interpretations to experimental facts to
the modeling of new problems in the natural sciences. Within the framework of a recently published article, we obtained the fractional
derivative of the variable concentration x(z), the effective mass of the electron dependent on the positionm(z) and the potential energy V (z),
produced by the confinement of the electron in a semiconductor of type AlxGa1¡xAs, with which we can intuit a possible geometric and
physical interpretation. As a consequence, it is proposed the existence of three physical and geometric conservative quantities approximate
character, associated with each of these parameters of the semiconductor, which add to the many physical magnitudes that already exist in
the literature within the context of fractional variation rates. Likewise, we find that the fractional derivatives of these magnitudes, apart from
having a common critical point, manifest self-similar behavior, which could characterize them as a type of fractal associated with the type of
semiconductor structures under study.
Original languageEnglish
Article number6
Pages (from-to)874-880
Number of pages6
JournalRevista Mexicana de Fisica
Volume66
Issue number6
StatePublished - 10 Nov 2020

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