  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.
