Study of the phi-generalized type k-fractional integrals or derivatives and some of their properties

Aydın M., Mahmudov N.

TURKISH JOURNAL OF MATHEMATICS, cilt.46, ss.1384-1396, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3906/mat-2110-51
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1384-1396
  • Anahtar Kelimeler: phi-generalized Riemann-Liouville k-fractional integral, phi-generalized Riemann-Liouville k-fractional derivative, phi-generalized Caputo k-fractional derivative, Cauchy type problem, RESPECT
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

A novel fractional integral in the sense of Riemann-Liouville integral and two new fractional derivatives in the sense of Riemann-Liouville derivative and Caputo derivative with respect to another function and two parameters are introduced. Some significant properties of them are presented like semigroup property, inverse property, etc. The solution of the Cauchy-type problem for the nonhomogenous linear differential equation with the phi-generalized Caputo k-fractional derivative is given by using the method of successive approximation.