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This article presents a comparative analysis of the conformable time–space fractional Fokker–Planck equation (TSF-FP equation) by operating two efficacious techniques: Fractional homotopy analysis transform method (FHATM) and conformable homotopy transform method (CHTM). The efficaciousness and validity of the proposed techniques are represented in terms of three different examples of conformable TSF-FP equations by computing various error norms: L2and absolute error. Convergence analysis of both techniques are studied theocratically and verified graphically as well. The findings demonstrate that for a given order of approximation CHTM requires less computational time in comparison to FHATM while FHATM is more general and converges faster than CHTM. The obtained information is confirmed graphically for different numerical values of fractional order.