Fundamental solutions for semidiscrete evolution equations via Banach algebras.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-07 DOI:10.1186/s13662-020-03206-7

Jorge González-Camus, Carlos Lizama, Pedro J Miana

引用次数: 11

Abstract

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.

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半离散演化方程的Banach代数基本解。

我们通过离散傅里叶变换给出了时间分数阶微分方程的解的表示，这些微分方程涉及由包含核的离散卷积定义的序列的勒贝格空间上的算子。考虑一阶和二阶有限差分算子，它们是一致连续半群和余弦函数的生成算子。给出了可和序列在Lebesgue空间中的线性和代数结构(特别是因子分解性质)及其范数和谱。我们确定了这些发电机的分数功率，并将从属原理应用于它们。我们还给出了一些应用和结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.