Analytic study of time-fractional Navier Stokes equation

This paper investigates the time fractional Navier Stokes equations involving the Caputo derivative and presents an analytic approximation based on the Homotopy Analysis Method (HAM). Fundamental concepts of fractional calculus and HAM are briefly reviewed, and a systematic LHAM framework is developed to construct convergent series solutions. Approximate analytic expressions are derived for different fractional orders α, and the influence of α on the velocity components is examined through numerical tables and graphical results. The obtained solutions demonstrate rapid convergence and clearly capture the memory effects intrinsic to fractional fluid flows, confirming the effectiveness of HAM for nonlinear time-fractional systems. The results provide a reliable semi analytical benchmark for future numerical studies of fractional Navier Stokes models