This thesis addresses these challenges by applying and extending the Optimal Homotopy Asymptotic Method (OHAM) to solve both linear and nonlinear FFDEs. The main contribution is the development of a generalized OHAM framework that incorporates advanced forms of fractional derivatives, specifically the Caputo-Katugampola (CK) derivative with two parameters and theAtangana–Baleanu–Caputo (ABC) derivative with Mittag–Leffler (ML) kernels involving three parameters.