A New Modified Integral Transform - Tidke, H. L.; Agrawal, Lina B. (Communications in Mathematics and Applications, 2025)
We introduce a new modified integral transform – a comprehensive extension encompassing the classical Laplace transform and its variants developed in recent decades. We establish its fundamental properties, including existence, linearity, scaling, shifting (both first and second), differentiation, integration, periodicity, and convolution. As a unifying framework, simplifies and generalizes various known integral transforms. We demonstrate its effectiveness through solutions to ordinary and partial differential equations, Volterra integral equations, partial integro-differential equations, and systems of ODEs, supported by illustrative examples.