A two-index generalization of conformable operatorswith potential applications in engineering and physics

• E. Reyes-Luis ^[3] ; G. Fernández-Anaya ^[3] ; J. Chávez- ^[1] ; L. Diago Cisneros ^[2] ; R. Muñoz Vega ^[1]
  1. [1] Universidad Autónoma de la Ciudad de México

     Universidad Autónoma de la Ciudad de México

     México

     
  2. [2] Universidad de La Habana

     Universidad de La Habana

     Cuba

     
  3. [3] niversidad Iberoamericana,Ciudad de México, México

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• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 67, Nº. 3, 2021, págs. 429-442
• Idioma: inglés
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• Resumen

  • We developed a somewhat novel fractional-order calculus workbench as a certain generalization of Khalil’s conformable derivative. Althoughevery integer-order derivate can naturally be consistent with fully physical-sense problem’s quotation, this is not the standard scenario of thenon-integer-order derivatives, even aiming physics systems’ modeling, solely. We revisited a particular case of the generalized conformablefractional derivative and derived a differential operator, whose properties overcome those of the integer-order derivatives, though preservingits 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 mathematicaltools, useful in generalizing widely accepted results, with potential applications to fundamental Physics within fractional order calculus. Thelatter seems to be especially appropriate for exercising the Sturm-Liouville eigenvalue problem, as well as the Euler-Lagrange equation, andto clarify several operator algebra matters.