Operational matrix method approach for fractional partial differential-equations

Turan Dincel A., Tural Polat S. N.

PHYSICA SCRIPTA, cilt.130724, ss.130724, 2024 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 130724
  • 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
  • Sayfa Sayıları: ss.130724
  • Yıldız Teknik Üniversitesi Adresli: Evet

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ACCEPTED MANUSCRIPT • The following article isOpen access

Operational matrix method approach for fractional partial differential-equations

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Accepted Manuscript online 6 November 2024 • © 2024 The Author(s). Published by IOP Publishing Ltd

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DOI 10.1088/1402-4896/ad8f7a

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Abstract

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.