@article{Ali2024, 
author = {Khalid K. Ali and Mohamed S. Mohamed and M. Maneea},
title = {A novel approach to  q-fractional partial differential equations: Unraveling solutions through semi-analytical methods},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {33442-33466},
keywords = {homotopy analysis method, fractional calculus, residual power series method, q-calculus, q-fractional partial differential equations, semi analytical techniques},
url = {https://www.sciopen.com/article/10.3934/math.20241596},
doi = {10.3934/math.20241596},
abstract = {This paper presents an innovative approach to solve  q-fractional partial differential equations through a combination of two semi-analytical techniques: The Residual Power Series Method (RPSM) and the Homotopy Analysis Method (HAM). Both methods are extended to obtain approximations for  q-fractional partial differential equations ( q-FPDEs). These equations are significant in  q-calculus, which has gained attention due to its relevance in engineering applications, particularly in quantum mechanics. In this study, we solve linear and nonlinear  q-FPDEs and obtain the closed-form solutions, which confirm the validity of the utilized methods. The results are further illustrated through two-dimensional and three-dimensional graphs, thus highlighting the interaction between parameters, particularly the fractional parameter, the  q-calculus parameter, and time.}
}