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In this article, thin film flow of non-Newtonian pseudo-plastic fluid is investigated on a vertical wall through homotopy-based scheme along with fractional calculus. Three cases were examined after considering (i) partial fractional differential equation (PFDE) by altering first-order derivative to fractional derivative in the interval (0, 1), (ii) PFDE by altering second-order derivative to fractional derivative in the interval (1, 2), and (iii) fully FDE by altering first-order derivative to fractional derivative in (0, 1) and second-order derivative to fractional derivative in (1, 2). Different physical quantities such as the velocity profile and volume flux were computed and analyzed. Validity of obtained results was checked by finding residuals. Moreover, consequence of different parameters on the velocity were also explored in fractional space.