On ?-Hilfer generalized proportional fractional operators
[ X ]
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Mathematical Sciences-Aims
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this paper, we introduce a generalized fractional operator in the setting of Hilfer fractional derivatives, the psi-Hilfer generalized proportional fractional derivative of a function with respect to another function. The proposed operator can be viewed as an interpolator between the Riemann-Liouville and Caputo generalized proportional fractional operators. The properties of the proposed operator are established under some classical and standard assumptions. As an application, we formulate a nonlinear fractional differential equation with a nonlocal initial condition and investigate its equivalence with Volterra integral equations, existence, and uniqueness of solutions. Finally, illustrative examples are given to demonstrate the theoretical results.
Açıklama
Anahtar Kelimeler
Hilfer fractional derivative, generalized proportional fractional derivative, existence and uniqueness, weighed space, fixed point theorems
Kaynak
Aims Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Cilt
7
Sayı
1
