Study of the φ-generalized type k-fractional integrals or derivatives and some of their properties
Turkish Journal of Mathematics, cilt.46, sa.4, ss.1384-1396, 2022 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: 4
- 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: Cauchy type problem, Φ-generalized caputo k -fractional derivative, Φ-generalized riemann-liouville k -fractional derivative, Φ-generalized riemann-liouville k -fractional integral
- Van Yüzüncü Yıl 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 φ-generalized Caputo k -fractional derivative is given by using the method of successive approximation