An approximate solution of a time fractional Burgers' equation involving the Caputo-Katugampola fractional derivative

The reduced version of the fractional Laplace transform, called the v-Laplac transform, is used in combination with the Adomian decomposition method to generate approximate solutions of the fractional Berger’s equation with the Caputo-Katugampola fractional derivative. The effect of the order of the Caputo-Katugampola fractional derivative in Berger’s equation is analyzed. The obtained approximate solutions are displayed graphically. The graphs and numerical solutions have demonstrated a tight correspondence between the exact and v-Laplace DM solutions. It is observed that the solutions for various orders u and v display the same behavior and tend to an integer-order problem’s solution, confirming the validity of the provided method.