Indexed by: Journal paper

First Author: Yongqiang Zhao

Correspondence Author: Yanbin Tang

Journal: Networks and Heterogeneous Media

Included Journals: SCI

Affiliation of Author(s): Huazhong University of Science & Technology

Place of Publication: USA

Discipline: Science

First-Level Discipline: Mathematics

Funded by: 国家自然科学基金

Document Type: J

Volume: 18

Issue: 3

Page Number: 1024–1058

ISSN No.: 1556-1801

DOI number: 10.3934/nhm.2023045

Date of Publication: 2023-03-24

Impact Factor: 1.41

Abstract: In this paper, we investigate the abstract integro-differential time-fractional wave equation with a small positive parameter ε. The Lp − Lq estimates for the resolvent operator family are obtained using the Laplace transform, the Mittag-Leffler operator family, and the C0−semigroup. These estimates serve as the foundation for some fixed point theorems that demonstrate the local-in-time existence of the solution in weighted function space. We first demonstrate that, for acceptable indices p ∈ [1, +∞) and s ∈ (1, +∞), the mild solution of the approximation problem converges to the solution of the associated limit problem in Lp((0, T), Ls(Rn)) as ε → 0+. The resolvent operator family and a set of kernel k(t) assumptions form the foundation of the proof’s primary methodology for evaluating norms. Moreover, we consider the asymptotic behavior of solutions as α → 2−.

Number of Words: 30000

Links to published journals: https://doi.org/10.3934/nhm.2023045