A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach

- The two-dimensional extended differential transform via local fractional derivative is first proposed.
- The theorems of the two-dimensional extended differential transform method are proved.
- The numerical solution for the local fractional diffusion equation is considered.
- The chart of the solution with non-differentiable terms is illustrated.

In this article, we first propose a new numerical technique based upon a certain two-dimensional extended differential transform via local fractional derivatives and derive its associated basic theorems and properties. One example of testing the local fractional diffusion equation is then considered. The numerical result presented here illustrates the efficiency and accuracy of the proposed computational technique in order to solve the partial differential equations involving local fractional derivatives.