TURKISH JOURNAL OF MATHEMATICS, vol.46, pp.1384-1396, 2022 (SCI-Expanded)
Article / Article
TURKISH JOURNAL OF MATHEMATICS
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
phi-generalized Riemann-Liouville k-fractional integral, phi-generalized Riemann-Liouville k-fractional derivative, phi-generalized Caputo k-fractional derivative, Cauchy type problem, RESPECT
Istanbul Technical University Affiliated:
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.