Abstract
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 n -dimensional case with applications to fractional convolution equations in the space S ′ ( R ̄ + n ) = S + ′ ( R ̄ + ) × S + ′ ( R ̄ + ) × ⋯ S + ′ ( R ̄ + ) .
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