Caputo Fractional Evolution Equations in Discrete Sequences Spaces

In 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.