Conformable Bilateral Laplace Transform on Time Scales

Abstract.

In this paper, we define the conformable bilateral Laplace transform on arbitrary time scales. We proved the decay property of the generalized exponential function as asymptotically approaches minus infinity. Then, the conditions for the absolute and uniform convergence of the conformable bilateral Laplace transform are provided. We specify the class of functions for which the transform exists and provide an inversion formula to reconstruct the original function on a time scale. Finally, the uniqueness theorem is proved for the proposed transform.