Fractional order Alpert multiwavelets for discretizing delay fractional differential equation of pantograph type

Hashemi M., Ashpazzadeh E., Moharrami M., Lakestanı M.

Applied Numerical Mathematics, cilt.170, ss.1-13, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 170
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.apnum.2021.07.015
  • Dergi Adı: Applied Numerical Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.1-13
  • Anahtar Kelimeler: Caputo derivative, Fractional pantograph differential equations, Fractional-order Alpert multiwavelets, Riemann–Liouville fractional integration
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this article, we develop a new set of functions called fractional-order Alpert multiwavelet functions to obtain the numerical solution of fractional pantograph differential equations (FPDEs). The fractional derivative of Caputo type is considered. Here we construct the Riemann–Liouville fractional operational matrix of integration (Riemann–Liouville FOMI) using the fractional-order Alpert multiwavelet functions. The most important feature behind the scheme using this technique is that the pantograph equation reduces to a system of linear or nonlinear algebraic equations. We perform the error analysis for the proposed technique. Illustrative examples are examined to demonstrate the important features of the new method.