The Variation Iteration Method Combined with the Natural Generalized Laplace Transform for Solving Fractional Burgers Equations

In this work, we solve fractional Burgers equations by using the new natural generalized Laplace transform (NGLT) and double natural generalized Laplace transform (DNGLT) methods with the variation iteration method. First, we present the basic definitions of natural transforms, the generalized Laplace transform, and Caputo fractional derivatives, which provide the theoretical basis of this work. This work is mainly concerned with the natural generalized Laplace variational iteration method (NGLTVIM), which is a new approach for the solution of conventional problems. The stability and convergence of the proposed method are discussed in detail to prove its reliability and effectiveness. The efficiency of the method for finding solutions to one-dimensional and singular fractional coupled Burgers equations is illustrated by several numerical examples. The results demonstrate that NGLTVIM can be successfully applied to solving various problems of mathematical physics.