Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
837502 | Nonlinear Analysis: Real World Applications | 2012 | 8 Pages |
The method of approximation of the tempered convolution based on Laguerre polynomials we are developing here applies to solving nonlinear fractional coupled systems appearing in mechanical (see Stojanović, 2011) [15]) and other fractional convolution equations from life and science (see Stojanović, 2011 [27]).In this paper, we use it as a tool in solving linear and nonlinear relaxation equations of distributed order with constant relaxation parameter, special weight functions, and with a lack of distributional solutions. We expand some special functions such as the Mittag-Leffler function into Laguerre series.A further perspective of a development of this method is generalization to the nn-dimensional case with applications to fractional convolution equations in the space S′(R̄+n)=S+′(R̄+)×S+′(R̄+)×⋯S+′(R̄+).