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In this paper, the extended direct algebraic approach with the general fractional derivative is employed to attain various novel wave structures of the non-linear fractional Tzitzéica type non-linear evolution equations in the form of kink, singular, periodic singular, dark, bright and dark-bright combine solitons. For the purpose to illustrate the physical behavior of the acquired solutions, some of the extracted results are sketched in the pattern of 3-D and 2-D plots which show the efficiency and authenticity of the proposed method. The under consideration method can also utilize to any other non-linear model appears in optics and engineering.