This chapter introduces the Guna-Raghav (GR) transform, a novel integral transform, and explores its various properties. The convolution theorem of the GR transform is presented, demonstrating its mathematical significance. Specifically, the chapter investigates the GR transform’s application in solving problems related to LR circuits, CR circuits, LCR circuits, and linear differential equations. Through illustrative examples in the domains of electrical circuits and linear systems, the chapter showcases the practical applications of the GR transform. The examples elucidate the transform’s effectiveness in addressing challenges encountered in the fields of electrical engineering and mathematical modeling. This comprehensive exploration aims to provide researchers and practitioners in the disciplines of electrical engineering and applied mathematics with valuable insights into the capabilities and potential applications of the GR transform.