Exponential Functions and Laplace Transforms for Alpha Derivatives
We introduce the exponential function for alpha derivatives on generalized time scales. We also define the Laplace transform that helps to solve higher order linear alpha dynamic equations on generalized time scales. If ® = ¾, the Hilger forward jump operator, then our theory contains the theory of delta dynamic equations on time scales as a special case. If ® = ½, the Hilger backward jump operator, then our theory contains the theory of nabla dynamic equations on time scales as a special case. Hence differential equations, difference equations (using the forward or backward difference operator), or q-difference equations (using the forward or backward q-difference operator) can be accommodated within our theory. We also present various properties of the Laplace transform and offer some examples.
E. Akin and M. Bohner, "Exponential Functions and Laplace Transforms for Alpha Derivatives," CRC Press, Jan 2004.
Mathematics and Statistics
Keywords and Phrases
Alpha derivative; Exponential function; Generalized time scale; Laplace Transform
Article - Conference proceedings
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