A new generalized Laplace transform and its applications to fractional Bagley-Torvik and fractional harmonic vibration problems

Abstract

. In this paper, a new generalized Laplace transform is defined and its certain properties are given. By using the new transform, the solutions of fractional Bagley-Torvik and fractional harmonic vibration problems are obtained, as application. Also transformations of some elementary functions and the relationships between the new transform with other generalized Laplace transforms are given in separate tables.