The subsurface deformation which is observed in seismic region during aseismic period has a great impact on displacement and stress-strain accumulation due to earthquake fault movement. In this paper we have considered a theoretical model of aseismically creeping, buried, inclined, infinite strike-slip fault located in viscoelastic half space of standard linear-solid medium. Our main objective is to find the analytical solutions of displacement, stresses, strains (a) in the absence of any fault movement and (b) after the commencement of fault movement with the help of Laplace transformation and Green’s function technique using fractional calculus taking Mittag-Leffler function and then to determine the numerical results of displacement, stresses and strains with different creep velocities for various inclinations of the fault using suitable model parametric values ([3], [7], [12], [26]). It is observed that the fault in our model exceeds the critical stress at about 117 years if it is a vertical fault while at about 141 years if the fault is inclined at an angle π/3 with the free surface. A comparative study has been done with the paper [24] and the numerical results are found to be in good agreement with it. This study may help in developing the earthquake prediction program.