TY  - JOUR
AU  - Ramadan, Mohamed A.
AU  - Abd El-Latif, Mahmoud A.
AU  - Alqarni, Mohammed Z.
PY  - 2025
TI  - An integrated Laplace transform and accelerated Adomian decomposition approach for solving time-fractional nonlinear partial differential equations
JO  - Electronic Research Archive
SP  - 4398
EP  - 4434
VL  - 33
IS  - 7
AB  - This study focuses on the efficient and accurate solution of time-fractional nonlinear partial differential equations (PDEs), which arise in various scientific and engineering applications but are often challenging to solve due to their complexity. We propose a novel method that integrates the Laplace transform with the accelerated Adomian decomposition method (AADM), forming the Laplace transform accelerated Adomian decomposition method (LAADM). The key innovation of this approach lies in its ability to handle the fractional time derivative expressed in the Caputo sense, while enhancing convergence speed and reducing computational effort. The methodology is systematically formulated, and several numerical experiments are conducted to validate its performance. The results demonstrate that LAADM provides highly accurate solutions and exhibits superior efficiency when compared to traditional solution techniques for fractional PDEs.
UR  - https://doi.org/10.3934/era.2025201
DO  - 10.3934/era.2025201