In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr...In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.展开更多
We use the modified Adomian decomposition method（ADM） for solving the nonlinear fractional boundary value problem {D α0＋u（x）=f（x,u（x）） ,0〈x〈1,3〈α≤4u（0）=α0, u″（0）=α2u（1）=β0,u″（1）β2where Dα...We use the modified Adomian decomposition method（ADM） for solving the nonlinear fractional boundary value problem {D α0＋u（x）=f（x,u（x）） ,0〈x〈1,3〈α≤4u（0）=α0, u″（0）=α2u（1）=β0,u″（1）β2where Dα 0 ＋u is Caputo fractional derivative and α0, α2, β0, β2 is not zero at all, and f ： [0, 1] × R→R is continuous. The calculated numerical results show reliability and efficiency of the algorithm given. The numerical procedure is tested on lineax and nonlinear problems.展开更多
基金Project supported by the Natural Science Foundation of Inner Mongolia of China (Grant No. 20080404MS0104)the Young Scientists Fund of Inner Mongolia University of China (Grant No. ND0811)
文摘In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.
文摘We use the modified Adomian decomposition method（ADM） for solving the nonlinear fractional boundary value problem {D α0＋u（x）=f（x,u（x）） ,0〈x〈1,3〈α≤4u（0）=α0, u″（0）=α2u（1）=β0,u″（1）β2where Dα 0 ＋u is Caputo fractional derivative and α0, α2, β0, β2 is not zero at all, and f ： [0, 1] × R→R is continuous. The calculated numerical results show reliability and efficiency of the algorithm given. The numerical procedure is tested on lineax and nonlinear problems.
