Numerical Solution of Nonlinear Fractional Bratu Equation with Hybrid Method

This work, we studied the Bratu differential equation of the fractional-order, numerically via introducing a hybrid method. This method is a combination of the Chebyshev polynomials and the block-pulse wavelets matrix of fractional order integration concerning the Caputo sense. Our approach transforms the nonlinear differential equation into a nonlinear algebraic system. We analyzed various forms of the fractional Bratu equation with different parameters of the equation and its fractional derivative orders. Besides, we show that the introduced method is convergent. We present the obtained results in tables and graphs. Based on these results, we can see the accuracy and convergence of the solutions. Since the Bratu equation is nonlinear so, based on the results obtained, we can say that the used method in approximating the solutions has acceptable accuracy and performance.