Fares, Bekhouche2026-10-062026-10-062026http://dspace.univ-khenchela.dz:4000/handle/123456789/11624This memoir deals with the solution of nonlinear fractional-time partial differen tial equations using the Residual Power Series Method (RPSM). The method is applied to the generalized Kuramoto–Sivashinsky (KS) equation, adopting the Ca puto time-fractional derivative of order α. The memoir is divided into three chap ters: the first chapter covers the fundamentals of fractional calculus and special functions, the second reviews the RPSM methodology and its convergence theory, while the third presents a numerical application to three test cases with different pa rameters and initial conditions. The resulting approximate solutions are compared with exact solutions and the results of other numerical methods through error ta bles and two- and three-dimensional graphical plots. The results demonstrate high accuracy, numerical stability, and low computational cost. They also highlight the memory effect induced by the fractional order α on wave behavior and temporal convergence, confirming the efficiency of the method in modeling complex phys ical phenomena such as flame fronts, thin liquid films, and plasma.enThesis