In recent years, fractal and multi-fractal analysis have been widely applied in many domains, especially in the field of image processing. In this direction we present in this paper a novel method for Arabic text-dependent writer identification based on fractal and multi-fractal features; thus, from the images of Arabic words, we calculate their fractal dimensions by using the "Box-counting" method, then we calculate their multi-fractal dimensions by using the method of DLA (Diffusion Limited Aggregates). To evaluate our method, we used 50 writers of the ADAB database, each writer wrote 288 words (24 Tunisian cities repeated 12 times) with 2/3 of words are used for the learning phase and the rest is used for the identification. The results obtained by using knearest neighbor classifier, demonstrate the effectiveness of our proposed method. Keywords-Fractal; Multi-Fractal; Arabic Writer Identification