In the present work, conditions are determined to guarantee the fulfilment of the_x000D_ fundamental theorem of calculus for fractional operators with fixed memory length._x000D_ The procedure followed to achieve the stated objective was to use the tools and tech niques of real analysis and fractional calculus to investigate the properties possessed_x000D_ by fractional operators with fixed memory length. Consequently, two function spaces_x000D_ were determined for whose elements the fundamental theorem of calculus for fractional_x000D_ operators with fixed memory length is verified