Solutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method

In this study, the explicit finite difference method is used to solve the fractional-order pseudo-hyperbolic telegraph partial differential equation by means of Caputo fractional derivative. A first-order finite difference approach is constructed for fractional order pseudo-hyperbolic telegraph partial differential equations. The difference scheme technique's stability estimate for the presented problem is given. The test problem is provided as an application. A comparison of the exact and approximate solutions is offered to determine the correctness and effectiveness of the suggested method. Finally, a graphical representation of the exact and approximate solutions in various cases is presented. The simulation of the obtained results are displayed in both the figures and the error analysis table.