2021/02/26 by Zeinab Toghani, Toghani, Zeinab, Luis Gaggero +1
Chemistry · Mathematics · #Advanced Differential Equations and Dynamical Systems #Applied mathematics #Chemistry #Derivative (finance) #Differential (mechanical device) #Economics #FOS: Mathematics #Finance #Fractional Differential Equations Solutions #Fractional calculus #Functional Analysis (math.FA) #Mathematics #Numerical methods for differential equations #Physics #Ring (chemistry) #Thermodynamics #math.FA
paper · pdf · doi:10.48550/arxiv.2102.13348
arxiv created 2021/02/26 · openalex publication_date 2021/02/26 · arxiv updated 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there is an infinite number of possible definitions of fractional derivatives, all are correct as differential operators each of which must be properly defined in its algebra. We introduce a generalized version of the fractional derivative that extends the existing ones in the literature. To those extensions, it is associated with a differentiable operator and a differential ring and applications that show the advantages of the generalization. We also review the different definitions of fractional derivatives proposed by Michele Caputo in \citeGJI:GJI529, Khalil, Al Horani, Yousef, Sababheh in \citekhalil2014new, Anderson and Ulness in \citeanderson2015newly, Guebbai and Ghiat in \citeguebbai2016new, Udita N. Katugampola in \citekatugampola2014new, Camrud in \citecamrud2016conformable and it is shown how the generalized version contains the previous ones as a particular case.