OICC Press Mathematical Analysis and its Contemporary Applications 7 3 2025 08 28 The novel hybrid approach for solving time-fractional Fokker-Planck equations by the Tarig projected differential transform method 10.30495/maca.2025.2063976.1141 EN Narsimhulu Dunna Department of Statistics and Applied Mathematics, Central University of Tamil Nadu, Neelakudi, Thiruvarur-610005, Tamil Nadu, India https://orcid.org/0000-0002-3698-9338 Athira Kinakkal Department of Statistics and Applied Mathematics, Central University of Tamil Nadu, Neelakudi, Thiruvarur-610005, Tamil Nadu, India Journal Article 2025 08 28 Fractional models offer greater accuracy and efficiency in modelling various physical systems across scientific, engineering, and technological fields. Analyzing linear and nonlinear time-fractional systems of fractional order differ- ential equations is a challenging task in terms of mathematical and theoretical aspects. In this paper, we propose a hybrid approach as a combination of the strength of the Tarig transform with the Projected Differential Transform Method (TPDTM) for solving the linear time-fractional Fokker-Planck (F-P) equation. The solution of the F-P equation was obtained in terms of space and fractional time co-ordinates based on imposing the different initial conditions. The results of the present work are illustrated using detailed 2D and 3D plots and tables for dif- ferent values of the fractional parameter, providing visual and numerical clarity on the behavior of the solutions. To validate the solution and evaluate the algorith- mic performance of the TPDTM, we have performed comparative analysis against solutions obtained using the Finite Difference Method (FDM), Homotopy Pertur- bation Method (HPM), and Laplace Adomian Decomposition Method (LADM) through different time fractional F-P equations. The study investigates solutions that show that TPDTM is a potent and straightforward technique for interpret- ing fractional F-P equations and is more versatile than FDM and HPM. Also, we found that our present work interpreted the high effectiveness and accuracy precision of results.