79323 20190709135634.0 doi 10.1016/j.jmaa.2016.12.006 sideral 97816 ART-2017-97816 eng (orcid)0000-0003-2453-7841 Abadias, Luciano Universidad de Zaragoza Non-local fractional derivatives. Discrete and continuous 2017 Access copy available to the general public Unrestricted We prove maximum and comparison principles for the discrete fractional derivatives in the integers. Regularity results when the space is a mesh of length h, and approximation theorems to the continuous fractional derivatives are shown. When the functions are good enough (Hölder continuous), these approximation procedures give a measure of the order of approximation. These results also allow us to prove the coincidence, for Hölder continuous functions, of the Marchaud and Grünwald–Letnikov derivatives in every point and the speed of convergence to the Grünwald–Letnikov derivative. The discrete fractional derivative will be also described as a Neumann–Dirichlet operator defined by a semi-discrete extension problem. Some operators related to the Harmonic Analysis associated to the discrete derivative will be also considered, in particular their behavior in the Lebesgue spaces lp(Z). info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.138 2017 MATHEMATICS 53 / 309 = 0.172 2017 Q1 T1 MATHEMATICS, APPLIED 99 / 252 = 0.393 2017 Q2 T2 1.103 2017 Applied Mathematics 2017 Q1 Analysis 2017 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion De León-Contreras, Marta Torrea, José L. 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 449, 1 (2017), 734-755 J. math. anal. appl. Journal of Mathematical Analysis and Applications 0022-247X 329730 http://zaguan.unizar.es/record/79323/files/texto_completo.pdf Postprint 32158 http://zaguan.unizar.es/record/79323/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:79323 articulos driver 2019-07-09-12:35:14 ARTICLE