TY - JOUR AU - S. O. Ajibola AU - E. O. Oghre AU - A. G. Ariwayo AU - P. O. Olatunji PY - 2021/05/22 Y2 - 2024/03/28 TI - On the Convergence of LHAM and its Application to Fractional Generalised Boussinesq Equations for Closed Form Solutions JF - Earthline Journal of Mathematical Sciences JA - EJMS VL - 7 IS - 1 SE - Articles DO - 10.34198/ejms.7121.2547 UR - https://earthlinepublishers.com/index.php/ejms/article/view/344 AB - By fractional generalised  Boussinesq equations we mean equations of the formwhere is a differentiable function and (to ensure nonlinearity). In this paper we lay emphasis on the cubic Boussinesq and Boussinesq-like equations of fractional order and we apply the Laplace homotopy analysis method (LHAM) for their rational and solitary wave solutions respectively. It is true that nonlinear fractional differential equations are often difficult to solve for their exact solutions and this single reason has prompted researchers over the years to come up with different methods and approach for their analytic approximate solutions. Most of these methods require huge computations which are sometimes complicated and a very good knowledge of computer aided softwares (CAS) are usually needed. To bridge this gap, we propose a method that  requires no linearization, perturbation or any particularly restrictive assumption that can be easily used to solve strongly nonlinear fractional differential equations by hand and simple computer computations with a very quick run time. For the closed form solution, we set  for each of the solutions and our  results  coincides with those of  others in the literature. ER -