LebesguE Regularity for Nonlocal Time-Discrete Equations with Delays

Leal, Claudio; Lizama, Carlos; Murillo‐Arcila, Marina

doi:10.1515/fca-2018-0037

Cited by 8 publications

(2 citation statements)

References 40 publications

(40 reference statements)

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“…Time‐discrete operators of fractional order appear in several areas of interest, in numerical analysis, as time‐stepping schemes of approximation for fractional evolution equations, 6,7 in the study of existence, uniqueness, and qualitative properties of fractional difference equations, 8–15 and in the analysis of mixed partial difference‐differential equations by means of operator theoretical methods, 16–20 among others.…”

Section: Introduction: Background and Main Resultsmentioning

confidence: 99%

Qualitative properties of nonlocal discrete operators

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Lizama

Rueda

2022

Math Methods in App Sciences

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In this article, we prove new convexity results for nonlocal discrete operators across an entire region that covers sequential orders in two parameters. We review and extend current studies on the properties of positivity, monotonicity, and convexity, explore borderline cases, and provide new insights on such properties by means of original examples evidencing the sharpness of the results. Our method is based on the novel principle of transference.

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Section: Introduction: Background and Main Resultsmentioning

confidence: 99%

Qualitative properties of nonlocal discrete operators

Bravo

Lizama

Rueda

2022

Math Methods in App Sciences

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“…is R-bounded [19]. See [6,15], [17]- [21] for further results on the corresponding quasi-linear equations.…”

Section: Introductionmentioning

confidence: 99%

Maximal regularity for fractional difference equations of order 2<alpha<3 on UMD spaces

Zhang,

2024

ejde

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In this article, we study the $\ell^p$-maximal regularity for the fractional difference equation $$ \Delta^{\alpha}u(n)=Tu(n)+f(n), \quad (n\in \mathbb{N}_0). $$ We introduce the notion of $\alpha$-resolvent sequence of bounded linear operators defined by the parameters $T$ and $\alpha$, which gives an explicit representation of the solution. Using Blunck's operator-valued Fourier multipliers theorems on $\ell^p(\mathbb{Z}; X)$, we give a characterization of the $\ell^p$-maximal regularity for $1 < p < \infty$ and $X$ is a UMD space. For more information see https://ejde.math.txstate.edu/Volumes/2024/20/abstr.html

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Maximal Regularity for Fractional Difference Equations with Finite Delay on UMD Spaces

Zhang,

2024

Mediterr. J. Math.

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LebesguE Regularity for Nonlocal Time-Discrete Equations with Delays

Cited by 8 publications

References 40 publications

Qualitative properties of nonlocal discrete operators

Qualitative properties of nonlocal discrete operators

Maximal regularity for fractional difference equations of order 2<alpha<3 on UMD spaces

Maximal Regularity for Fractional Difference Equations with Finite Delay on UMD Spaces

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