On the Convergence of LHAM and its Application to Fractional Generalised Boussinesq Equations for Closed Form Solutions

  • S. O. Ajibola Department of Mathematics, University of Benin, Nigeria
  • E. O. Oghre Department of Mathematics, University of Benin, Nigeria
  • A. G. Ariwayo Department of Mathematical Sciences, Adekunle Ajasin University, Nigeria
  • P. O. Olatunji Department of Mathematical Sciences, Adekunle Ajasin University, Nigeria
Keywords: fractional calculus, Laplace homotopy analysis method, Boussinesq equations, closed form solution


By fractional generalised  Boussinesq equations we mean equations of the form


where 2021-05-22_13_45_11-Adobe_Acrobat_Professional_-_[EJMS070120212547.pdf]_.png is a differentiable function and 2021-05-22_13_45_24-Adobe_Acrobat_Professional_-_[EJMS070120212547.pdf]_.png (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 2021-05-22_13_45_41-Adobe_Acrobat_Professional_-_[EJMS070120212547.pdf]_.png for each of the solutions and our  results  coincides with those of  others in the literature.


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How to Cite
Ajibola, S. O., Oghre, E. O., Ariwayo, A. G., & Olatunji, P. O. (2021). On the Convergence of LHAM and its Application to Fractional Generalised Boussinesq Equations for Closed Form Solutions. Earthline Journal of Mathematical Sciences, 7(1), 25-47. https://doi.org/10.34198/ejms.7121.2547