Abstract

REYES-LUIS, E. et al. A two-index generalization of conformable operators with potential applications in engineering and physics. Rev. mex. fis. [online]. 2021, vol.67, n.3, pp.429-442.  Epub Feb 21, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.67.429.

We developed a somewhat novel fractional-order calculus workbench as a certain generalization of Khalil’s conformable derivative. Although every integer-order derivate can naturally be consistent with fully physical-sense problem’s quotation, this is not the standard scenario of the non-integer-order derivatives, even aiming physics systems’ modeling, solely. We revisited a particular case of the generalized conformable fractional derivative and derived a differential operator, whose properties overcome those of the integer-order derivatives, though preserving its clue advantages. Worthwhile noting that the two-fractional indexes differential operator we are dealing with departs from the single-fractional index framework, which typifies the generalized conformable fractional derivative. This distinction leads to proper mathematical tools, useful in generalizing widely accepted results, with potential applications to fundamental Physics within fractional order calculus. The latter seems to be especially appropriate for exercising the Sturm-Liouville eigenvalue problem, as well as the Euler-Lagrange equation, and to clarify several operator algebra matters.

Keywords : Conformable operators; algebraic methods; quantum operators; sturm Liouville operator.

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