OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 8 01 2025 07 13 A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation 10.71932/ EN Elham Afshari Young Researcher Club, khomein Branch, Islamic Azad University, Khomein, Iran. Journal Article 2025 07 13 In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in the Caputo sense. We propose a new finite difference method for solving time fractional diffu- sion equation. In our method firstly, we transform the Caputo derivative into Riemann-Liovill derivative. The stability and convergence of this method are investigated by a Fourier analysis. We show that this method is uncondition- ally stable and convergent with the convergence order O( 2+h2), where t and h are time and space steps respectively. Finally, a numerical example is given that confirms our theoretical analysis and the behavior of error is examined to verify the order of convergence.