AN EXTENDED LAPLACE INTEGRAL TRANSFORM AND ITS APPLICATIONS

In this paper, we introduce a new integral transform, called an extended Laplace integral transform, and also investigate its properties like linearity property, first and second shifting property, change of scale property, convolution theorem, and derivative property. Moreover, we obtain an extended Laplace integral transform of some elementary functions. Furthermore, we demonstrate an extended Laplace integral transform in solving ordinary and partial differential equations through different examples. We also introduce a new application of an extended Laplace integral transform for Volterra integral equations, Volterra integro-differential equations, and Caputo fractional-order differential equations. Finally, by replacing some parameters appropriately, an extended Laplace integral transform is reduced to several integral transforms known in the literature as special cases.