New determination of the fractural derivative of its properties

• Anis F. Galimyanov ^[1] ; Radik M. Askhatov ^[1] ; Diana V. Demidova ^[1]
  1. [1] Kazan Federal University

     Kazan Federal University

     Rusia

     
• Localización: Revista Inclusiones: Revista de Humanidades y Ciencias Sociales, ISSN-e 0719-4706, Vol. 6, Nº. Extra 16 (julio-septiembre), 2019 (Ejemplar dedicado a: Nuevos Avances y Miradas de la Ciencia III), págs. 270-282
• Idioma: inglés
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• Resumen

  • The article aims to present a new definition of the fractional derivative of a function by replacing the exponential function with an increasing logarithmic function. In addition to the introduced definition, proof of relevance and the need to introduce a new fractional derivative, the properties of the fractional derivative and their proof are considered. All the properties of the introduced fractional derivative are proved, similar to the properties of the ordinary derivative. Also, fractional derivatives in the indicated sense are calculated for some elementary functions. The article discusses fractional derivative theorems necessary for solving fractional integral and differential equations.