Lie symmetry analysis, explicit solutions, and conservation laws of the time-fractional Fisher equation in two-dimensional space

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• The Lie point symmetries of the time-fractional Fisher equation are utilized and derived. • The technique of the power series is applied to conclude the explicit solutions for the time-fractional Fisher equation for the first time. • The conservation laws for the time-fractional Fisher equation are built using a novel conservation theorem. • Several graphical countenances were utilized to award a visual performance of the obtained solutions. In these analyses, we consider the time-fractional Fisher equation in two-dimensional space. Through the use of the Riemann-Liouville derivative approach, the well-known Lie point symmetries of the utilized equation are derived. Herein, we overturn the fractional fisher model to a fractional differential equation of nonlinear type by considering its Lie point symmetries. The diminutive equation's derivative is in the Erdélyi-Kober sense, whilst we use the technique of the power series to conclude explicit solutions for the diminutive equations for the first time. The conservation laws for the dominant equation are built using a novel conservation theorem. Several graphical countenances were utilized to award a visual performance of the obtained solutions. Finally, some concluding remarks and future recommendations are utilized.