Integral transformations are one of the most important requirements of our modern era from a practical standpoint, because through them we can find all solutions to complex equations that do not have a solution according to specific initial conditions, and the human need is primarily for those solutions, as 60% of the equations we can solve using integration and predict future solutions. Because it requires a lot of limitations for those answers, prediction is one of the most challenging aspects of the modeling process Integral transforms have shown to be an effective tool for resolving mathematical issues in a variety of practical contexts and scientific domains, including chemistry, biology, physics, and technology. In this study, we develop transformational integrals in a new way, called “ \({{\varvec{A}}}_{{\varvec{T}}}\) transform” and investigate their definitions and basic theorems. The \({{\varvec{A}}}_{{\varvec{T}}}\) transform was used in this study to predict the solutions of equations that do not have a solution and it proved effective in those solutions.