In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE). The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM). The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically.

In the electrical discharge machining (EDM) process, especially during the machining of hardened steels, changes in tool shape have been identified as one of the major problems. To understand the aforesaid dilemma, an initiative was undertaken through this experimental study. To assess the distortion in tool shape that occurs during the machining of EN31 tool steel, variations in tool shape were examined by monitoring the roundness of the tooltip before and after machining with a coordinate measuring machine. The change in out-of-roundness of the tooltip varied from 5.65 to 37.8 µm during machining under different experimental conditions. It was revealed that the input current, the pulse on time, and the pulse off time had most significant effect in terms of changes in the out-of-roundness values during machining. Machine learning techniques (decision tree, random forest, generalized linear model, and neural network) were applied for the prediction of changes in tool shape. It was observed that the results predicted by the random forest technique were more convincing. Subsequently, it was gathered from this examination that the usage of the random forest technique for the prediction of changes in tool shape yielded propitious outcomes, with high accuracy (93.67%), correlation (0.97), coefficient of determination (0.94), and mean absolute error (1.65 µm) values. Hence, it was inferred that the random forest technique provided better results in terms of the prediction of tool shape.

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

In electrical discharge machining (EDM), the machined surface quality can be affected by the excessive temperature generation during the machining process. To achieve a longer life of the finished part, the machined surface quality plays a key role in maintaining its overall integrity. Surface roughness is an important quality evaluation of a material’s surface that has considerable influence on mechanical performance of the material. Herein, a sintered cermet tooltip with 75% copper and 25% titanium carbide was used as tool electrode for processing H13 steel. The experiments have been performed to investigate the effects of EDM parameters on the machined surface roughness. The findings show that, as the pulse current, pulse length, and pulse interval are increased, the surface roughness tends to rise. The most significant determinant for surface roughness was found to be pulse current. A semi-empirical surface roughness model was created using the characteristics of the EDM technique. Buckingham’s theorem was used to develop a semi-empirical surface roughness prediction model. The semi-empirical model’s predictions were in good agreement with the experimental studies, and the built empirical model based on physical features of the cermet tooltip was tested using dimensional analysis.