<p>Movement on faults plays a crucial role in defining how stress is stored or released in seismically active regions. 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 for a finite, creeping dip-slip fault inclined in a viscoelastic half-space characterized by a fractional Burger rheology. Laplace transformation for fractional derivatives, a Modified Green’s function technique, the correspondence principle and finally inverse Laplace transformation have been used to derive analytical solutions for displacement, stress, and strain components. The graphical representations were used 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. 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 help to study the subsurface deformation and its effect on fault movement, causing earthquakes.</p>