Baleanu, DumitruOdibat, Zaid2020-02-122025-09-182020-02-122025-09-182019Odibat, Zaid; Baleanu, Dumitru, "A linearization-based approach of homotopy analysis method for non-linear time-fractional parabolic PDEs", Mathematical Methods in the Applied Sciences, Vol. 42, No. 18, (2019).0170-42141099-1476https://doi.org/10.1002/mma.5829https://hdl.handle.net/20.500.12416/10809Odibat, Zaid/0000-0002-2414-7969In this paper, a novel approach, namely, the linearization-based approach of homotopy analysis method, to analytically treat non-linear time-fractional PDEs is proposed. The presented approach suggests a new optimized structure of the homotopy series solution based on a linear approximation of the non-linear problem. A comparative study between the proposed approach and standard homotopy analysis approach is illustrated by solving two examples involving non-linear time-fractional parabolic PDEs. The performed numerical simulations demonstrate that the linearization-based approach reduces the computational complexity and improves the performance of the homotopy analysis method.eninfo:eu-repo/semantics/closedAccessHomotopy Analysis MethodLinearization-Based Approach Of HamSeries SolutionTime-Fractional Parabolic PdeArticle10.1002/mma.58292-s2.0-85070754552