Abstract
The foundation of this study lies in the fractional order derivative definition pioneered by Caputo and Fabrizio, with distinct representations for temporal and spatial variables. Our focus is on presenting a finite element scheme to address the time-fractional diffusion equation. This approach contrasts with traditional finite difference methods and variational solutions. We rigorously establish the stability and convergence order of our proposed method. To validate our theoretical assertions, we provide a numerical example demonstrating its efficacy.
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