Note on the generalized conformable derivative

• Alberto Fleitas ^[1] ; J.E. Nápoles Valdés ^[2] ; J.M. Rodríguez ^[3] ; J.M. Sigarreta-Almira ^[1]
  1. [1] Universidad Autónoma de Guerrero

     Universidad Autónoma de Guerrero

     México

     
  2. [2] Universidad Nacional del Nordeste

     Universidad Nacional del Nordeste

     Argentina

     
  3. [3] Universidad Carlos III de Madrid

     Universidad Carlos III de Madrid

     Madrid, España

     

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 2, 2021, págs. 443-457
• Idioma: inglés
• DOI: 10.33044/revuma.1930
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• Resumen

  • We introduce a definition of a generalized conformable derivative of order α > 0 (where this parameter does not need to be integer), with which we overcome some deficiencies of known local derivatives, conformable or not. This definition allows us to compute fractional derivatives of functions defined on any open set on the real line (and not just on the positive halfline). Moreover, we extend some classical results to the context of fractional derivatives. Also, we obtain results for the case α > 1.