The novel hybrid approach for solving time-fractional Fokker-Planck equations by the Tarig projected differential transform method

Dunna, Narsimhulu; Kinakkal, Athira

doi:10.30495/maca.2025.2063976.1141

The novel hybrid approach for solving time-fractional Fokker-Planck equations by the Tarig projected differential transform method

10.30495/maca.2025.2063976.1141

Volume 7, Issue 3
Summer 2025

Pages 77-113

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Narsimhulu Dunna

Athira Kinakkal

Department of Statistics and Applied Mathematics, Central University of Tamil Nadu, Neelakudi, Thiruvarur-610005, Tamil Nadu, India

Abstract

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 differential 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 different values of the fractional parameter, providing visual and numerical clarity on the behavior of the solutions. To validate the solution and evaluate the algorithmic performance of the TPDTM, we have performed comparative analysis against solutions obtained using the Finite Difference Method (FDM), Homotopy Perturbation 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 interpreting 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.

Keywords

Fractional differential calculus

Fokker-Planck equation

Tarig transform

Projected differential transform method

Numerical simulation

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