Haar wavelet method for solution of variable order linear fractional integro-differential equations

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Amin R., Shah K., Ahmad H., Ganie A. H., Abdel-Aty A., Botmart T.

AIMS Mathematics, cilt.7, sa.4, ss.5431-5443, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3934/math.2022301
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.5431-5443
  • Anahtar Kelimeler: variable-order fractional calculus, fixed-point theory, Gauss elimination method, Haar wavelet, numerical approximation
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

In this paper, we developed a computational Haar collocation scheme for the solution of fractional linear integro-differential equations of variable order. Fractional derivatives of variable order is described in the Caputo sense. The given problem is transformed into a system of algebraic equations using the proposed Haar technique. The results are obtained by solving this system with the Gauss elimination algorithm. Some examples are given to demonstrate the convergence of Haar collocation technique. For different collocation points, maximum absolute and mean square root errors are computed. The results demonstrate that the Haar approach is efficient for solving these equations.