Abstract
We provided two different approaches for solving fractional-order diffusion equations in this article. The fractional Atangana-Baleanu derivative operator in addition to the Laplace transform is used to generate several new approximate-analytical solutions to the time-fractional diffusion equations. The implementation of a sophisticated and straightforward approach to solving diffusion equations having a fractional-order derivative is the motivation and uniqueness behind the current work. The solutions to some illustrative problems are calculated to ensure that the actual and approximate solutions to the targeted problems are in close contact. The results we obtained have a higher rate of convergence and provide a closed-form solution, according to analysis. The proposed method’s key advantage is the small amount of calculations required. The suggested techniques can be applied to nonlinear fractional-order problems in a variety of applied science areas due to their simple and straightforward implementation. It can be used to overcome specific fractional-order physical problems in a variety of fields of applied sciences.