A robust study via semi-analytical approach for fractional telegraph equation

Abstract

The present study uses iterative Shehu Transform Adomian Decomposition Method to tackle fractional Telegraph equation in $1D$, $2D$, and $3D$, respectively. These equations are particularly notable in field of material science and a few other related fields. A graphical compatibility of approx. and exact results is used to test the efficacy and validity of proposed technique. $2D$ and $3D$ graphs are provided to show a compatible technique of approximate-exact findings. Without any linearization or discretization, iterative Shehu ADM methodology offers a reliable and efficient way to provide approximations and accurate solutions that are error-free. The theoretical and numerical convergence aspects are also validated in this study. It is noticed that on increasing number of grid points, the $L_{\infty }$ error norm got reduced which is a valid claim for numerical convergence.