Abstract Spin lattice relaxation is the simplest type of β NMR measurement. The usual approach to implant a pulse hyperpolarized nuclei and monitor time-resolved β-decay asymmetry, yielding ensemble average spin-lattice relaxation. In case, asymmetry decays exponentially with characteristic time constant T 1 , but this ideal rarely obtained in practice. most data, more complicated. This can be ...

In this paper, we apply the Laplace decomposition method to obtain a series solutions of the Burgers-Huxley and Burgers-Fisher equations. The technique is based on the application of Laplace transform to nonlinear partial differential equations. The method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

In this paper we present the development of a rigorous approach for the solution of non-linear partial differential equations by use of the Laplace transformation — in particular, the convolution theorem for Laplace transforms. While the rigor of this new approach is general, our paper is devoted to the development, verification, and application of this method for the case of real gas flow in p...

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

in this paper, inverse laplace transform method is applied to analytical solution of the fractional sturm-liouville problems. the method introduces a powerful tool for solving the eigenvalues of the fractional sturm-liouville problems. the results  how that the simplicity and efficiency of this method.