Numerical solution of fractional Bratu type equations with Legendre reproducing kernel method

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 and convergence of iterative process are shown by orthogonal projection operator. Numerical results show that our method is effective and convenient for fractional Bratu type problem.