Progress in Fractional Differentiation & Applications

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Applying a new fractional derivative, the Λ- fractional derivative, with the corresponding Λ-fractional space, fractional differential geometry is discussed. The Λ-fractional derivative satisfies the conditions for the existence of a differential, demanded by the differential topology, in the Λ-fractional space, where the Λ-derivatives behave like the conventional ones. Thus, fractional differential geometry is established in that Λ -space in the conventional way. The results are pulled back to the initial space. The present work concerns the geometry of fractional curves and surfaces.

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