SOLUTION OF FRACTIONAL BURGERS EQUATION BY TWO INTEGRAL TRANSFORM BASED SEMI ANALYTICAL METHODS

This study is concerned with the solution to a family of problems in mathematical physics referred to as Burgers equation. The fractional order Burgers equation considered is a nonlinear problem and can therefore not be solved by using any of the known analytical methods. Two hybrid methods are proposed for its solution; Shehu transform homotopy analysis method and Shehu transform Adomian decomposition method. The integral transform adopted, apart from generalizing the earlier transforms such as Laplace transform and Sumudu transform, it equally has the advantage of solving variable coefficients problems. After applying Shehu transform to every term in the given equation with the fractional order derivative interpreted in Caputo-Fabrizio sense, homotopy derivatives in homotopy analysis method and Adomian polynomials are respectively used to overcome the nonlinearities in the problem. Once that is accomplished, the inverse Shehu transform is taken to get the desired solution. These proposed methods are applied to solve some problems in literature, and the solutions those in the referenced literature. The results are tabulated and as well plotted in 3D graphs for ease of comparison. All the computations are carried out using Mathematica 13.0.