Adaptation of reproducing kernel method in solving Atangana-Baleanu fractional Bratu model

In this analysis, a reliable computational technique is implemented for the solution of fractional-order initial and boundary value problems of Bratu-type equations, called reproducing kernel method. The model under consideration is endowed with Atangana-Baleanu fractional derivative. The proposed technique is developed to create an exact solution in a convergent series formula in terms of the Atangana-Baleanu operator with easily calculable components. By means of reproducing kernel theory, an iterative operational algorithm is built for dealing with the fractional Bratu-type equations. Furthermore, the convergence and stability analysis of the method is discussed. To these aims, meaningful numerical examples are included to demonstrate the feasibility and reliability of this technique and to test the qualitative effect of using the Atangana-Baleanu operator on the quality of the acquired accounts. Also, a numerical comparison is made with some common numerical methods. From a numerical viewpoint, the gained results clearly show a high level of accuracy and great technical skills of the proposed method of dealing with such types of nonlinear fractional equations.