Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method

Sakar M. G., Uludağ F., Erdoğan F.

APPLIED MATHEMATICAL MODELLING, vol.40, pp.6639-6649, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40
  • Publication Date: 2016
  • Doi Number: 10.1016/j.apm.2016.02.005
  • Journal Name: APPLIED MATHEMATICAL MODELLING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.6639-6649
  • Keywords: Homotopy perturbation method, Fractional partial differential equation, Proportional delay, Caputo derivative, DIFFERENTIAL-EQUATIONS, DIFFUSION-EQUATIONS, ITERATION METHOD, WAVE, CALCULUS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of α are presented graphically.

In this paper, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x. The method do not require linearization or small perturbation. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of alpha are presented graphically. (C) 2016 Elsevier Inc. All rights reserved.