Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate

  • Onur SaldırEmail author
  • Mehmet Giyas Sakar
  • Fevzi Erdogan


We present a new approach depending on reproducing kernel method (RKM) for time-fractional Kawahara equation with variable coefficient. This approach consists of obtaining an orthonormal basis function on specific Hilbert spaces. In this regard, some special Hilbert spaces are defined. Kernel functions of these special spaces are given and basis functions are obtained. The approximate solution is attained as serial form. Convergence analysis, error estimation and stability analysis are presented after obtaining the approximate solution. To show the power and effect of the method, two examples are solved and the results are given as table and graphics. The results demonstrate that the presented method is very efficient and convenient for Kawahara equation with fractional order.


Reproducing kernel method Kawahara equation Caputo derivative Convergence 

Mathematics Subject Classification

65M12 35R11 46E22 



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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  • Onur Saldır
    • 1
    Email author
  • Mehmet Giyas Sakar
    • 1
  • Fevzi Erdogan
    • 2
  1. 1.Department of Mathematics, Faculty of SciencesVan Yuzuncu Yil UniversityVanTurkey
  2. 2.Department of Statistics, Faculty of SciencesVan Yuzuncu Yil UniversityVanTurkey

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