The seismically active regions often correlate with fault lines, and the movement of these faults plays a crucial role in defining how stress is stored or released in these areas. To investigate the deformation and accumulation/release of stress and strain in seismically active regions during the aseismic period, a mathematical model has been developed by considering a finite, creeping dip-slip fault inclined in the viscoelastic half-space of a fractional Burger rheology. Laplace transformation for fractional derivatives, Modified Green's function technique, correspondence principle and finally, the inverse Laplace transformation have been used to derive analytical solutions for displacement, stress and strain components. The graphical representations were depicted using MATLAB to understand the effect on displacement, stresses and strains due to changes in inclinations and creep velocities of the fault, as well as orders of the fractional derivative. Our investigation indicates that a change in creep velocity and inclination of the fault has a significant effect, while a change in the order of fractional derivative has a moderate effect on displacement, stress, and strain components. Analysis of these results can provide insights into subsurface deformation and its impact on fault movement, which can lead to earthquakes.