Fundamental solutions for semidiscrete evolution equations via Banach algebras

Advances in Difference Equations

article

González-Camus, Jorge¹  Lizama, Carlos¹  Miana, Pedro J.² 

[1] Departamento de Matemáticas y Ciencias de la Computación, Universidad de Santiago de Chile;Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza

关键词: Caputo fractional derivative;    Discrete fractional Laplacian;    Discrete fractional operators;    Fundamental solutions;    Wright and Mittag-Leffler functions;   

DOI  :  10.1186/s13662-020-03206-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which are generators of uniformly continuous semigroups and cosine functions. We present the linear and algebraic structures (in particular, factorization properties) and their norms and spectra in the Lebesgue space of summable sequences. We identify fractional powers of these generators and apply to them the subordination principle. We also give some applications and consequences of our results.

【 授权许可】

CC BY