ON THE SOLUTION OF BRATU'S INITIAL VALUE PROBLEM IN THE LIOUVILLE-CAPUTO SENSE BY ARA TRANSFORM AND DECOMPOSITION METHOD

In this paper, a new method which is a linear combination of ARA transform and the decomposition method is proposed to establish the solution of Bratu's initial value problem in the Liouville-Caputo sense. First of all, ARA transform and its inverse transform are utilized to reduce the problem into a algebraic equation. Later, by using the decomposition method the numerical solution is established in the series form. Finally, an illustrative example is presented to reveal the implementation of the method. The outcomes illustrate the accuracy and efficiency of the method.