A note on linear non-Newtonian Volterra integral equations

GÜNGÖR N.

Mathematical Sciences, cilt.16, sa.4, ss.373-387, 2022 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s40096-021-00427-z
  • Dergi Adı: Mathematical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.373-387
  • Anahtar Kelimeler: Adomian decomposition method, Non-Newtonian calculus, Non-Newtonian Volterra integral equations, Successive approximations method, ∗ -resolvent kernel method
  • Samsun Üniversitesi Adresli: Hayır

Özet

In this study, the Volterra integral equations are defined in the non-Newtonian calculus with the aid of ∗ -integral. The focus of this study is obtaining the solution of linear non-Newtonian integral equations. The ∗ -resolvent kernel method, successive approximations method and Adomian decomposition method are applied for solving non-Newtonian integral equations in the non-Newtonian sense. Some numerical examples are presented to explain the procedure of these methods. Finally, a model that describes a type of the exponential growth model is proposed in the sense of non-Newtonian calculus as an example.