Analytical treatments of time-fractional seventh-order nonlinear equations via Elzaki transform

Liaqat Ali, Guang Zou*, Na Li, Kashif Mehmood, Pan Fang, Adnan Khan

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


In this article, we’ll show how to solve the time-fractional seventh-order Lax’s Korteweg–de Vries and Kaup–Kupershmidt equations analytically using the homotopy perturbation approach, the Adomian decomposition method, and the Elzaki transformation. The KdV equation is a general integrable equation with an inverse scattering transform-based solution that arises in a variety of physical applications, including surface water waves, internal waves in a density stratified fluid, plasma waves, Rossby waves, and magma flow. Fractional derivative is described in the Caputo sense. The solutions to fractional partial differential equation is computed using convergent series. The numerical computations and graphical representations of the analytical results obtained using the homotopy perturbation and decomposition techniques. Moreover, plots that are simple to grasp are used to compare the integer order and fractional-order solutions. After only a few iterations, we may easily obtain numerical results that provide us better approximations. The exact solutions and the derived solutions were observed to be very similar. The suggested methods have also acquired the highest level of accuracy. The most prevalent and convergent techniques for resolving nonlinear fractional-order partial differential issues are the applied techniques.

Original languageEnglish
Article number1
Number of pages30
JournalJournal of Engineering Mathematics
Issue number1
Publication statusPublished - 2024

Bibliographical note

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Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • 26A33
  • 34A25
  • 35A20
  • 35Q53
  • Analytical techniques
  • Caputo operator
  • Elzaki Transform
  • Kaup–Kupershmidt (KK) equation
  • Lax’s Korteweg–de Vries equation


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