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

Abstract

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.

Keywords

• Pseudo-hyperbolic telegraph equation
• Finite difference method
• Caputo fractional derivative
• Stability
• Approximate solution
• Error estimate