Abstract
A function f(t) is called original function if:
-
1.
f(t) ≡ 0 for t < 0,
-
2.
\(|f(t)| < Me^{s_0t}\) for t > 0 with \(M > 0, s_0\in \mathbb {R}\).
-
3.
For every closed interval [a, b], the function satisfies the Dirichlet conditions:
-
(a)
is bounded,
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(b)
or is continuous, or has a finite number of discontinuities of first kind,
-
(c)
has a finite number of extremes.
-
(a)
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Notes
- 1.
Pierre Laplace (1749–1827).
- 2.
E. Post (1897–1954).
- 3.
J. Stirling (1692–1770).
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Milici, C., Drăgănescu, G., Tenreiro Machado, J. (2019). The Laplace Transform. In: Introduction to Fractional Differential Equations. Nonlinear Systems and Complexity, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-030-00895-6_3
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