• Nitin Sachan
• Diwari Lal

This paper gives a comparative evaluation of the effectiveness of two numerical methods, namely the Fractional Reduced Differential Transform Method (FRDTM) and the Finite Difference Method (FDM), in the process of solving the time fractional telegraph equation (TFTE). The TFTE is a mathematical model that has numerous applications in a variety of domains, including engineering and physics, among others. The purpose of this study is to investigate and evaluate the performance of FRDTM and FDM with regard to the accuracy, stability, and computational efficiency of the two methods. First, a concise introduction to the TFTE and the significance of its solutions in practical applications is provided. This is followed by the main body of the paper. Following that, the numerical techniques known as FRDTM and FDM are presented and described in further detail. A series of numerical experiments are carried out in order to carry out the comparison analysis. These experiments take into consideration a variety of scenarios and parameter values. To decide the degree of precision, the mathematical arrangements are analyzed against insightful arrangements that are now known. The results of the comparison study provide useful insights into the strengths and limits of FRDTM and FDM when applied to time fractional telegraph equations. Those academics and practitioners who are looking for optimal numerical solutions for issues that are governed by such equations will find this information to be critically important. The research makes a contribution to the continuing discussion over the selection of acceptable numerical methods for fractional differential equations. It also advances our understanding of the application and performance of these approaches in situations that occur in the real world.

TFTE, FRDTM, Approximation Techniques, Efficient Approximations, Fractional Derivative

"Assessing the Efficacy of FRDTM and FDM in Solving Time Fractional Telegraph Equations: A Comparative Study", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 3, page no.g676-g685, March-2024, Available :http://www.jetir.org/papers/JETIR2403691.pdf

"Assessing the Efficacy of FRDTM and FDM in Solving Time Fractional Telegraph Equations: A Comparative Study", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 3, page no. ppg676-g685, March-2024, Available at : http://www.jetir.org/papers/JETIR2403691.pdf