Existence and numerical analysis using Haar wavelet for fourth-order multi-term fractional differential equations

Amin R., Shah K., Mlaiki N., YÜZBAŞI Ş., Abdeljawad T., Hussain A.

Computational and Applied Mathematics, vol.41, no.7, 2022 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1007/s40314-022-02041-8
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: Fixed-point theory, Fractional calculus, Gauss elimination method, Haar wavelet, Numerical approximation
  • Akdeniz University Affiliated: Yes

Abstract

© 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.In this paper, a numerical technique is developed for the solution of multi-term fractional differential equations (FDEs) upto fourth order by using Haar collocation method (HCM). In Caputo sense, the fractional derivative is defined. The integral involved in the equations is calculated by the method of Lepik. The HCM converts the given multi-term FDEs into a system of linear equations. The convergence of the proposed method HCM is checked on some problems. Mean square root and maximum absolute errors are calculated for different numbers of collocation points(CPs), which are recorded in tables. The exact and approximate solution comparison is also given in figures. The time taken by CPU for numerical results is also given in the tables.