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We first demonstrate that, for acceptable indices $ p\\in[1, +\\infty) $ and $ s\\in(1, +\\infty) $, the mild solution of the approximation problem converges to the solution of the associated limit problem in $ L^{p}((0, T), L^{s}({\\bf R}^{n})) $ as $ \\varepsilon\\rightarrow 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 $ \\alpha\\rightarrow 2^{-} $.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023045","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T10:38:24Z","timestamp":1679654304000},"page":"1024-1058","source":"Crossref","is-referenced-by-count":3,"title":["Approximation of solutions to integro-differential time fractional wave equations in $ L^{p}- $space"],"prefix":"10.3934","volume":"18","author":[{"given":"Yongqiang","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China"}]},{"given":"Yanbin","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China"},{"name":"Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023045-1","unstructured":"J. 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