Fractional evolution equations in dicrete sequences spaces

Abstract

In this talk, we consider fractional differential equations (in the sense of Caputo) on the sequence Lebesgue spaces ℓ 𝑝 (Z) with 𝑝 1. The associated operator to the Cauchy problem is defined by convolution with a sequence of compact support. We use techniques from Functional Analysis to calculate the solution of the problem. In the case of fractional powers of operators, we give explicitly the solution of the problem. As a consequence, we obtain new integral formulae for certain special functions.