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 ħ
In the past few decades, fractional-order calculus has emerged as a potential tool in various domains of science and engineering such as fluid dynamic traffic, neurophysiology [1], potential theory, control theory, viscoelasticity, electromagnetic theory, bioengineering, electric technology, plasma physics and mathematical economy. Real-world processes, which we deal with, are normally of fractional order. Heat diffusion into a semi-infinite solid where heat flow equals the half-derivative of the temperature is an example of a fractional-order system.
