Abstract
At the outset of this chapter we will be concerned with the (delta) Laplace transform, which is a special case of the Laplace transform studied in the book by Bohner and Peterson [62]. We will not assume the reader has any knowledge of the material in that book. The delta Laplace transform is equivalent under a transformation to the Z-transform, but we prefer the definition of the Laplace transform given here, which has the property that many of the Laplace transform formulas will be analogous to the Laplace transform formulas in the continuous setting. We will show how we can use the (delta) Laplace transform to solve initial value problems for difference equations and to solve summation equations. We then develop the discrete delta fractional calculus. Finally, we apply the Laplace transform method to solve fractional initial value problems and fractional summation equations.
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Goodrich, C., Peterson, A.C. (2015). Discrete Delta Fractional Calculus and Laplace Transforms. In: Discrete Fractional Calculus. Springer, Cham. https://doi.org/10.1007/978-3-319-25562-0_2
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DOI: https://doi.org/10.1007/978-3-319-25562-0_2
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