مشخصات پژوهش

Time-fractional Fokker–Planck models are essential for describing anomalous diffusion, stochastic processes with memory, and transport phenomena in fields such as physics, biology, finance, and engineering. Their fractional nature introduces non-locality and memory effects, making analytical solutions rare and standard numerical methods often inefficient, inaccurate, or unstable, particularly for long-time simulations. Traditional discretization-based techniques typically require fine meshes and small time steps, leading to high computational costs and error accumulation. This creates a strong necessity for high-accuracy and efficient numerical methods tailored for fractional models. The spectral–series approach using Chebyshev polynomials offers a powerful alternative, as spectral methods are well-known for their exponential convergence, stability, and ability to capture global solution behavior with fewer basis functions. The importance of this research lies in providing a robust and computationally efficient framework for solving time-fractional Fokker–Planck equations, thereby advancing theoretical studies and enabling more precise simulations in diverse scientific and engineering applications.