BRINI KhadidjaBENAISSA Abdelkader2026-09-092026-09-092026https://dspace.univ-temouchent.edu.dz/handle/123456789/7494Wave equation with fractional derivative in generalized Caputo sense is investigated. In this thesis, we analyze the Cauchy problem in Rn with linear fractional damping (frictional). First, we establish the system’s well-posedness through semi group theory, ensuring the existence and uniqueness of solutions, named the quantitative results. In addition, we show the strong stability of our system, where qualitative results are obtained by applying the general criterion of Arendt and Batty fombined with C0-semi group approach.frThesis