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 calculus extends usual derivation. operator, associated to Cauchy problem, is defined by a convolution of compact support and belongs Banach algebra ℓ1(Z). We in detail these sequences. use techniques from algebras Functional Analysis explicity check solution problem.