Modified Laplace-type Transform and Its Properties

In this article, we introduce the Modified Laplace-type transform, develop convergence properties, and obtain fundamental formulas of some elementary functions such as power functions, sine, cosine, hyperbolic sine, hyperbolic cosine, and exponential functions. We derive translation theorems and a scale-preserving theorem and also show the relationship between the modified Laplace type transform and the modified degenerate Gamma function. This integral transform is applied to solve linear ordinary differential equations with constant coefficients and a Volterra integral equation of the second kind.