Authors: A.A. Hemeda
Addresses: Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
Abstract: In this work, the new iterative method and Picard method are prepared to solve nonlinear fractional differential equations such as the fractional gas dynamics equation and the fractional coupled Burgers' equations. The fractional derivatives and integrals are considered in the Riemann-Liouvill and Caputo sense. Comparisons between the two methods and also between their results are made. The results obtained by these methods are in high agreement with the corresponding exact solutions with little number of iterations and hence these methods may be considered an alternative and efficient methods for finding approximate solutions for nonlinear fractional differential equations. The advantages of these methods are that there is no need to calculate Adomian's polynomials or Lagrange's multiplier values also they can be used without linearisation or small perturbation. The solutions obtained by these methods show that the methods are easy to implement and computationally very attractive.
Keywords: new iterative method; NIM; Picard method; fractional calculus; fractional gas dynamics; fractional coupled Burgers' equations; nonlinear differential equations; fractional differential equations.
International Journal of Mathematical Modelling and Numerical Optimisation, 2015 Vol.6 No.4, pp.282 - 298
Received: 14 May 2015
Accepted: 12 Aug 2015
Published online: 28 Dec 2015 *