000079323 001__ 79323 000079323 005__ 20190709135634.0 000079323 0247_ $$2doi$$a10.1016/j.jmaa.2016.12.006 000079323 0248_ $$2sideral$$a97816 000079323 037__ $$aART-2017-97816 000079323 041__ $$aeng 000079323 100__ $$0(orcid)0000-0003-2453-7841$$aAbadias, Luciano$$uUniversidad de Zaragoza 000079323 245__ $$aNon-local fractional derivatives. Discrete and continuous 000079323 260__ $$c2017 000079323 5060_ $$aAccess copy available to the general public$$fUnrestricted 000079323 5203_ $$aWe 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). 000079323 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000079323 590__ $$a1.138$$b2017 000079323 591__ $$aMATHEMATICS$$b53 / 309 = 0.172$$c2017$$dQ1$$eT1 000079323 591__ $$aMATHEMATICS, APPLIED$$b99 / 252 = 0.393$$c2017$$dQ2$$eT2 000079323 592__ $$a1.103$$b2017 000079323 593__ $$aApplied Mathematics$$c2017$$dQ1 000079323 593__ $$aAnalysis$$c2017$$dQ2 000079323 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000079323 700__ $$aDe León-Contreras, Marta 000079323 700__ $$aTorrea, José L. 000079323 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000079323 773__ $$g449, 1 (2017), 734-755$$pJ. math. anal. appl.$$tJournal of Mathematical Analysis and Applications$$x0022-247X 000079323 8564_ $$s329730$$uhttps://zaguan.unizar.es/record/79323/files/texto_completo.pdf$$yPostprint 000079323 8564_ $$s32158$$uhttps://zaguan.unizar.es/record/79323/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000079323 909CO $$ooai:zaguan.unizar.es:79323$$particulos$$pdriver 000079323 951__ $$a2019-07-09-12:35:14 000079323 980__ $$aARTICLE