Gegenbauer wavelet solutions of fractional integro-differential equations

Özaltun G., Konuralp A., Gümgüm S.

Journal of Computational and Applied Mathematics, cilt.420, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 420
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.cam.2022.114830
  • Dergi Adı: Journal of Computational and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Integro-differential equations, Gegenbauer wavelets, Orthonormal polynomials, Approximate solution, Fractional derivative
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

The aim of this study is to use Gegenbauer wavelets in the solution of fractional integro-differential equations. The method is applied to several problems with different values of resolution parameter and the degree of the truncated polynomial. The results are compared with those obtained from other numerical methods. We observe that the current method is very effective and gives accurate results. One of the reasons for that is it enables us to improve accuracy by increasing resolution parameter, while keeping the degree of polynomial fixed. Another reason is nonlinear terms do not require linearization. Hence the method can be directly implemented and results in the system of algebraic equations which solved by Wolfram Mathematica. It can be asserted that this is the first application of the Gegenbauer wavelet method to the aforementioned types of problems.