doi:10.3390/foundations2040059engMahillo, AlejandroMiana, Pedro J.Caputo fractional evolution equations in discrete sequences spacesART-2022-130707In this paper, we treat some fractional differential equations on the sequence Lebesgue spaces ℓp(N0) with p≥1. The Caputo fractional calculus extends the usual derivation. The operator, associated to the Cauchy problem, is defined by a convolution with a sequence of compact support and belongs to the Banach algebra ℓ1(Z). We treat in detail some of these compact support sequences. We use techniques from Banach algebras and a Functional Analysis to explicity check the solution of the problem.2022http://zaguan.unizar.es/record/11979510.3390/foundations2040059http://zaguan.unizar.es/record/119795oai:zaguan.unizar.es:119795Foundations 2, 4 (2022), 872-884byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess