Numerical simulation of space-fractional Helmholtz equation arising in seismic wave propagation, imaging and inversion

In this paper, a reliable numerical scheme, the q-fractional homotopy analysis transform method (q-FHATM), is proposed to examine the Helmholtz equation of fractional order arising in seismic wave propagation, imaging and inversion. Sufficient conditions for its convergence and error estimates are established. The q-FHATM provides a solution in a rapidly convergent series. Results for different fractional values of space derivatives are compared with the existing methods and discussed with the help of figures. A proper selection of parameters yields approximations identical to the exact solution. Parameter offers an expedient way of controlling the region of convergence of the solution. Test examples are provided to illustrate the accuracy and competency of the proposed scheme. The outcomes divulge that our scheme is attractive, user-friendly, reliable and highly effective.