Salim Zidi2026-09-092026-07-06https://dspace.univ-tebessa.dz/handle/123456789/412This thesis aims to investigate a space-fractional variant of the conven- tional Lengyel–Epstein CIMA reaction model. Initially, we establish the global existence, uniqueness, and boundedness of solutions. We then ex- amine the system’s main analytical properties. Subsequently, we derive the conditions on the reactor size and diffusion coefficient that preclude the exis- tence of non-constant positive steady-state solutions. We further analyze the stability of the constant steady-state solution for both the ODE and PDE models. Finally, we establish sufficient conditions for the global asymp- totic stability of the positive steady-state solution using the direct Lyapunov method.enfractional reaction–diffusion systemsasymptotic stabilityLya- punov functionalglobal and local stability of solutionsThesis