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*Foundations*, Volume 2, Issue 4 (December 2022) – 19 articles

**Cover Story**(view full-size image): 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 with the Cauchy problem, is defined by a convolution with a sequence of compact support and belongs to the Banach algebra ℓ1(Z). We treat some of these compact support sequences in detail. We use techniques from Banach algebras and a functional analysis to explicitly check the solution of the problem. View this paper

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