Caputo Fractional Evolution Equations in Discrete Sequences Spaces

Mahillo, Alejandro; Miana, Pedro J.

doi:10.3390/foundations2040059

Open AccessArticle

Caputo Fractional Evolution Equations in Discrete Sequences Spaces

by

Alejandro Mahillo

^†

and

Pedro J. Miana

^*,†

Calle Pedro Cerbuna 12, Departamento de Matemáticas, IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Foundations 2022, 2(4), 872-884; https://doi.org/10.3390/foundations2040059

Submission received: 30 August 2022 / Revised: 20 September 2022 / Accepted: 26 September 2022 / Published: 11 October 2022

(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions)

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Abstract

In this paper, we treat some fractional differential equations on the sequence Lebesgue spaces

ℓ^{p} (N_{0})

with

p \geq 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

ℓ^{1} (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.

Keywords: Caputo fractional derivation; convolution product; Banach algebras

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MDPI and ACS Style

Mahillo, A.; Miana, P.J. Caputo Fractional Evolution Equations in Discrete Sequences Spaces. Foundations 2022, 2, 872-884. https://doi.org/10.3390/foundations2040059

AMA Style

Mahillo A, Miana PJ. Caputo Fractional Evolution Equations in Discrete Sequences Spaces. Foundations. 2022; 2(4):872-884. https://doi.org/10.3390/foundations2040059

Chicago/Turabian Style

Mahillo, Alejandro, and Pedro J. Miana. 2022. "Caputo Fractional Evolution Equations in Discrete Sequences Spaces" Foundations 2, no. 4: 872-884. https://doi.org/10.3390/foundations2040059

APA Style

Mahillo, A., & Miana, P. J. (2022). Caputo Fractional Evolution Equations in Discrete Sequences Spaces. Foundations, 2(4), 872-884. https://doi.org/10.3390/foundations2040059

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Caputo Fractional Evolution Equations in Discrete Sequences Spaces

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