an:06997097
Zbl 1407.65214
Hosseinpour, Soleiman; Nazemi, Alireza; Tohidi, Emran
A new approach for solving a class of delay fractional partial differential equations
EN
Mediterr. J. Math. 15, No. 6, Paper No. 218, 20 p. (2018).
00425149
2018
j
65M70 35R11 44A10 42C10 65D32 33C45
delay fractional partial differential equations; operational matrix; M??ntz polynomials; pseudospectral method; Pad?? approximation; two-sided Laplace transformations
Summary: In this article, a new numerical approach has been proposed for solving a class of delay time-fractional partial differential equations. The approximate solutions of these equations are considered as linear combinations of M??ntz-Legendre polynomials with unknown coefficients. Operational matrix of fractional differentiation is provided to accelerate computations of the proposed method. Using Pad?? approximation and two-sided Laplace transformations, the mentioned delay fractional partial differential equations will be transformed to a sequence of fractional partial differential equations without delay. The localization process is based on the space-time collocation in some appropriate points to reduce the fractional partial differential equations into the associated system of algebraic equations which can be solved by some robust iterative solvers. Some numerical examples are also given to confirm the accuracy of the presented numerical scheme. Our results approved decisive preference of the M??ntz-Legendre polynomials with respect to the Legendre polynomials.