Semi-analytical analysis of Allen-Cahn model with a new fractional derivative

Deniz S.

Mathematical Methods in the Applied Sciences, vol.44, no.3, pp.2355-2363, 2021 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Abstract
  • Volume: 44 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.5892
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2355-2363
  • Keywords: Allen-Cahn model, Atangana-Baleanu derivative, optimal perturbation iteration method
  • Manisa Celal Bayar University Affiliated: No

Abstract

The Allen-Cahn model equation is extended to the fractional form by using Atangana-Baleanu derivative. The modified nonlinear equation is analyzed via optimal perturbation iteration technique and Laplace transform. Some new analytical approximate solutions are derived for different cases of order α. Absolute residual errors of different order of approximations are presented to check the effectiveness and power of the proposed method and new derivative.