SAIAH SEYYID ALI2026-06-142026-06-142026-06-04https://dspace.univ-chlef.dz/handle/123456789/2474THÈSE Présentée pour l’obtention du diplôme de DOCTORAT LMD Filière : Mathématiques Spécialité :Analyse Mathématique Par SAIAH SEYYID ALIIn this thesis, we are interested to study Global existence of small data solutions to some semilinear σ-evolution models. The main goal of this study is to clarify the effect of the influence of parameters and the data onthe rang and qualitative properties of solutions. Using modified Bessel functions and the Mittag-Leffler function, we show some polynomial decay Lm − Lq estimates of Sobolev solutions to related linear models with vanishing right-hand side. We explain connections between the fractional orders and the exponents, which allow to prove the global (in time) existence of small-data Sobolev solutions by applying the fixed-point argumentenThesis