Abstract
The Laplace transform and its inverse constitute a powerful technique for solving linear differential equations. This approach to solving such equations, when combined with complex analysis, provides one of the most formidable tools in the analyst’s tool kit. In the next few lectures we review how this approach can be applied to fractional differential equations with constant coefficients having rational and irrational exponents. In this way we find that the solutions to such equations can be written as series of generalized exponentials and in so doing make contact with our earlier lectures.
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