Further properties of the Laplace transform on time scales with arbitrary graininess

Abstract

In this work, we generalize several properties of the usual Laplace transform to the Laplace transform on arbitrary time scales. Among them are translation theorems, transforms of periodic functions, integration of transforms, transforms of derivatives and integrals, and asymptotic values.

Keywords:

• time scales
• Laplace transform
• time scale exponential function
• translation theorems

AMS Subject Classification :

• 44A10
• 34N05
• 26E70
• 39A10
• 39A12
• 39A13