@article{Barkat2025, 
author = {Omar Barkat and Awatif Muflih Alqahtani},
title = {Analytical solutions for fractional Navier–Stokes equation using residual power series with        ϕ  -Caputo generalized fractional derivative},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {15476-15496},
keywords = {ϕ-Caputo fractional derivative, Caputo–Hadamard fractional derivative, residual power series, fractional Navier–Stokes equation},
url = {https://www.sciopen.com/article/10.3934/math.2025694},
doi = {10.3934/math.2025694},
abstract = {In this study, we aimed to derive analytical solutions for a system of nonlinear time-fractional Navier–Stokes equations in Cartesian coordinates by employing the residual power series method. Moreover, we showed that the    ϕ-Caputo fractional derivative describes these equations in time, enabling the Riemann-Liouville, Hadamard, and Katugampola fractional derivatives to be generalized into a unified form. Additionally, we provide results for certain cases that are given in the literature. Therefore, the solutions obtained for the time-fractional Navier–Stokes equations are presented graphically in the Caputo–Hadamard sense.}
}