Numerical Solution of Fractional Bratu Type Equations with Legendre Reproducing Kernel Method

  • Mehmet Giyas SakarEmail author
  • Onur Saldır
  • Ali Akgül
Original Paper


In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert space theory with shifted Legendre polynomials. Construction of iterative process is shown by orthogonal projection operator. Numerical results show that our method is effective and convenient for fractional Bratu type problem.


Bratu equation Reproducing kernel method Shifted Legendre polynomials Boundary value problem Numerical approximation 


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© Springer Nature India Private Limited 2018

Authors and Affiliations

  1. 1.Faculty of Sciences, Department of MathematicsYuzuncu Yil UniversityVanTurkey
  2. 2.Faculty of Art and Sciences, Department of MathematicsSiirt UniversitySiirtTurkey

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