Comparison of two reliable methods to solve fractional Rosenau-Hyman equation

Senol M., TAŞBOZAN O., Kurt A.

Mathematical Methods in the Applied Sciences, cilt.44, sa.10, ss.7904-7914, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Özet
  • Cilt numarası: 44 Sayı: 10
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1002/mma.5497
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: 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
  • Sayfa Sayıları: ss.7904-7914
  • Anahtar Kelimeler: Caputo fractional derivative, fractional partial differential equations, perturbation-iteration algorithm, residual power series method
  • Hatay Mustafa Kemal Üniversitesi Adresli: Evet

Özet

In this study, we examine the numerical solutions of the time-fractional Rosenau-Hyman equation, which is a KdV-like model. This model demonstrates the formation of patterns in liquid drops. For this purpose, two reliable methods, residual power series method (RPSM) and perturbation-iteration algorithm (PIA), are used to obtain approximate solutions of the model. The fractional derivative is taken in the Caputo sense. Obtained results are compared with each other and the exact solutions both numerically and graphically. The outcome shows that both methods are easy to implement, powerful, and reliable. So they are ready to implement for a variety of partial fractional differential equations.