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In this paper, we develop a new time-space fractional constitution relation to study the unsteady boundary layer flow over a stretching sheet. For the convenience of calculation, the boundary layer flow is simulated as a symmetrical rectangular area. The implicit difference method combined with an L1-algorithm and shift Grünwald scheme is used to obtain the numerical solutions of the fractional governing equation. The validity and solvability of the present numerical method are analyzed systematically. The numerical results show that the thickness of the velocity boundary layer increases with an increase in the space fractional parameter <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>. For a different stress fractional parameter <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, the viscoelastic fluid will exhibit viscous or elastic behavior, respectively. Furthermore, the numerical method in this study is validated and can be extended to other time-space fractional boundary layer models.