@article{Al-Mazmumy2025, 
author = {Mariam Al-Mazmumy and Mona Alsulami and Norah AL-Yazidi},
title = {Algorithms and applications of the new modified decomposition method to solve initial-boundary value problems for fractional partial differential equations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {5806-5829},
keywords = {fractional differential equations, advanced decomposition method, initial and boundary value conditions, Riemann–Liouville derivative, Caputo derivative},
url = {https://www.sciopen.com/article/10.3934/math.2025267},
doi = {10.3934/math.2025267},
abstract = {This study aims to efficiently solve the class of initial-boundary problems for fractional partial differential equations by expanding the modified Adomian decomposition method. Three new algorithms are proposed, two for handling various fractional initial-boundary problems via the    x-differential operator, and one for using the    t-differential operator. The proposed methods are designed to increase computational efficiency and ensure greater accuracy in the solutions. The effectiveness of the techniques is reviewed by applying them to a variety of cases, demonstrating their ability to address a broad range of fractional calculus problems. The results emphasize the flexibility and adaptability of the developed algorithms as reliable methods.}
}