@article{Zhao2023, 
author = {Yongqiang Zhao and Yanbin Tang},
title = {Approximation of solutions to integro-differential time fractional wave equations in        L          p        −space},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {3},
pages = {1024-1058},
keywords = {time fractional derivative, integro-differential equation, time fractional wave equation, heterogeneous parameter, homogeneous limit problem, analytic semigroup, C0semigroup},
url = {https://www.sciopen.com/article/10.3934/nhm.2023045},
doi = {10.3934/nhm.2023045},
abstract = {In this paper, we investigate the abstract integro-differential time-fractional wave equation with a small positive parameter    ε. The        L          p        −      L          q       estimates for the resolvent operator family are obtained using the Laplace transform, the Mittag-Leffler operator family, and the        C          0        −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        L          p        (  (  0  ,  T  )  ,      L          s        (            R              n        )  ) 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          −      .}
}