Displaying similar documents to “The use of fractional B-splines wavelets in multiterms fractional ordinary differential equations.”

A detailed analysis for the fundamental solution of fractional vibration equation

Li-Li Liu, Jun-Sheng Duan (2015)

Open Mathematics

Similarity:

In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...

On Fractional Helmholtz Equations

Samuel, M., Thomas, Anitha (2010)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 26A33, 33E12, 33C60, 35R11 In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.