A New Approach for the Fractional Rosenau–Hyman Problem by ARA Transform

ÇETİNKAYA S., DEMİR A.

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1002/mma.10934
  • 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
  • Keywords: Caputo fractional derivative ARA transform, Daftardar–Gejji and Jafari iteration method, Rosenau–Hyman problem
  • Kocaeli University Affiliated: Yes

Abstract

The primary aim of this research to establish the solution to time fractional Rosenau–Hyman problem (RHP) by utilizing a new approach including ARA transform and Daftardar–Gejji and Jafari iteration method (DGJIM). The fractional derivative is taken in Caputo sense. First, employing ARA and its inverse transform leads the problem to a simpler one. Second, utilization of DGJIM yields the approximate solutions to the problem in series form, which leads to the analytical solution. The novelty of this research is the analytic solution to time fractional RHP with the help of pattern relation among the approximate solutions by proposed method. To the best knowledge of authors, the analytical solution to time fractional RHP has not been established by any research. The obtained outcomes confirm that the proposed method is accurate and effective to deal with nonlinear fractional problems.