In one space-and in one time -dimension a beam-like equation is solved, where the second time derivative is replaced by the a?fractional time derivative, 1 <α< 2. The solution is given in closed form in terms of the Mttag-Leffler functions in two parameters.
In this paper, a first order semi-discrete method of a partial integro-differential equation with a weakly singular kernel is considered. We apply Galerkin spectral method in one direction, and the inversion technique for the Laplace transform in another direction, the result of the numerical experiment proves the accuracy of this method.
Yu Zongshan Zeng Youdong (College of Math, and Computer Science, Fuzhou University, Fuzhou 350002)
