Article ID Journal Published Year Pages File Type
9506329 Applied Mathematics and Computation 2005 10 Pages PDF
Abstract
Fractional calculus generalizes the derivative and antiderivative operations dn/dzn of differential and integral calculus from integer orders n to the entire complex plane. Methods are presented for using this generalized calculus with Laplace transforms of complex-order derivatives to solve analytically many differential equations in physics, facilitate numerical computations, and generate new infinite-series representations of functions. As examples, new exact analytic solutions of differential equations, including new generalized Bessel equations with complex-power-law variable coefficients, are derived.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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