Operational matrix method approach for fractional partial differential-equations

TURAN DİNCEL A., TURAL POLAT S. N.

Physica Scripta, cilt.99, sa.12, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 99 Sayı: 12
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1088/1402-4896/ad8f7a
  • Dergi Adı: Physica Scripta
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: fractional partial differential equations, hermite wavelets, operational matrix, sylvester equations
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Fractional partial differential equations (FPDEs) have become very popular to model and analyze numerous different physical phenomena in recent years. However, it is generally complicated to find the exact solutions of those FPDEs. The objective of this study is to find the approximate numerical solution of FPDEs by introducing a wavelet-based operational matrix technique. In this study we employ Hermite wavelets (HWs) and the operational matrices of the fractional integration for Hermite wavelets. The sparsity of the obtained operational matrices provides fast and efficient computation of the proposed method. The original FPDE equations are converted to Sylvester equations, which then are solved to obtain the final solution. We provide a few numerical examples to demonstrate the versatility and efficiency of the proposed method.