New Analytical Solutions for Klein-Gordon and Helmholtz Equations in Fractal Dimensional Space

Abstract

We consider the local fractional Klein Gordon equation and Helmholtz equation in (1+1) fractal dimensional space. The local fractional Laplace series expansion method is used to solve the local fractional partial differential equations in fractal dimensional space. We present the non differentiable analytical solutions and the corresponding graphs. The obtained results illustrate the accuracy and efficiency of this approach to local fractional partial differential equations.