| Summary: | This paper presents an efficacious analytical and numerical method for solution of fractional differential equations. This technique, here in named <i>q</i>-HATM (<i>q</i>-homotopy analysis transform method) is applied to a one-dimensional fractional Fornberg–Whitham model and a two-dimensional fractional population model emanating from biological sciences. The overwhelming agreement of our analytical solution by the <i>q</i>-HATM technique with the exact solution indeed establishes the efficacy of <i>q</i>-HATM to solve the fractional Fornberg–Whitham model and the two-dimensional fractional population model. Furthermore, comparisons by means of extensive analysis using numerics, graphs and error analysis are presented to affirm the preference of <i>q</i>-HATM technique over other methods. A variant of the <i>q</i>-HATM using symmetry can also be considered to solve these problems.
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