Abstract:
This study focused on solving fractional acoustic wave equations, which are essential for understanding
systems characterized by long-range interactions or anomalous diffusion. Fractional differential
equations (FDEs), which generalize ordinary differential equations by incorporating fractional
derivatives or integrals, were the primary mathematical framework used. The Homotopy
Analysis Method (HAM) and Homotopy Perturbation Method(HPM) are semi-analytical technique
renowned for its capability in solving nonlinear differential equations, were employed to derive
exact solutions for these FDEs. By applying both HAM and HPM exact solutions for the fractional
acoustic wave equations were successfully obtained and illustrated graphically. The results
demonstrated the effectiveness and efficiency of HAM and HPM in solving fractional differential
equations. Homotopy Perturbation Method is only a special case of the homotopy analysis method.
Both methods are in principle based on Taylor series with respect to an embedding parameter. Besides,
both can give very good approximations by means of a few terms, if initial guess and auxiliary
linear operator are good enough. This underscores the methods are potential and powerful tools
for researchers addressing complex systems that exhibit non-standard dynamic behaviors, thereby
broadening the scope of analytical techniques available for studying such phenomena. Comparative
analysis is conducted between the results obtained through HAM and HPM. This comparison
helps in validating the methods and showcasing their respective strengths and potential limitations
