10.1007/s40096-022-00491-z

Numerical and analytical solution to a conformable fractional Fornberg–Whitham equation

  • Cyril D. Enyi1,
  • Eze R. Nwaeze*2,
  • McSylvester E. Omaba1,
  1. Department of Mathematics, University of Hafr Al Batin, Hafar Al Batin, SA
  2. Department of Mathematics and Computer Science, Alabama State University, Montgomery, US

Published in Issue 2022-09-24

How to Cite

Enyi, C. D., Nwaeze, E. R., & Omaba, M. E. (2022). Numerical and analytical solution to a conformable fractional Fornberg–Whitham equation. Mathematical Sciences, 18(2 (June 2024). https://doi.org/10.1007/s40096-022-00491-z
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Abstract

Abstract In this work, we perform a broader analytical and numerical study of a space-time conformable fractional Fornberg–Whitham equation. The concept of conformable fractional Laplace transform was infused in the well-known homotopy analysis method (HAM), to obtain a more accurate solution. We named this method q -Homotopy Analysis Conformable Fractional Laplace Transform Method ( q -HACFLTM). In addition, thorough numerical analysis using graphs and error analysis confirms that q -HACFLTM performs better and more accurately than the q -HAM technique previously applied to solve this problem. Moreover, the proposed method eliminates any form of restriction on the fractional order of the derivatives as was the case in the previous work of Iyiola and Ojo (Pramana J Phys 58(4): 567–575, 2005). Our method ( q -HACFLTM) is quite easy and highly accurate and could be adopted for use in solving other fractional differential equation models, once similar properties of Laplace transform used here could be established. The q -HACFLTM technique applied here does not require any perturbation, discretization, polynomials or Lagrange multiplier, thus giving it some advantage over methods like ADM, HPTM or VIM, etc. The Laplace transform introduced was able to handle the nonlinear terms of the equation in a more robust manner, resulting in more accurate solution and faster convergence.

Keywords

  • Laplace transform,
  • q-homotopy analysis transform method,
  • Fornberg–Whitham equation,
  • Conformable fractional derivative

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