On a Fractional Operator Combining Proportional and Classical Differintegrals
[ X ]
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function f(t), by a fractional integral operator applied to the derivative f ' (t). We define a new fractional operator by substituting for this f ' (t) a more general proportional derivative. This new operator can also be written as a Riemann-Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann-Liouville integral and a Caputo derivative. We then conduct some analysis of the new definition: constructing its inverse operator and Laplace transform, solving some fractional differential equations using it, and linking it with a recently described bivariate Mittag-Leffler function.
Açıklama
Anahtar Kelimeler
fractional integrals, Caputo fractional derivatives, fractional differential equations, bivariate Mittag-Leffler functions, 26A33, 34A08
Kaynak
Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
8
Sayı
3
