Turkish Journal of Mathematics
Abstract
In the most general case of $\omega$-weights, some normed functional spaces $% X_{\omega}^{p}(a,b)( 1\leq p\leq\infty)$, $AC_{\gamma,\omega}^n[a,b]$ and a generalization of the fractional integro-differentiation operator are introduced and analyzed. The boundedness of the $\omega$-weighted fractional operator over $X_{\omega}^{p}(a,b)$ is proved. Some theorems and lemmas on the properties of the invertions of the mentioned operator and several representations of functions from $AC_{\gamma,\omega}^n[a,b]$ are established. A general $\omega$-weighted Caputo fractional derivative of order $\alpha$ is studied over $AC_{\gamma,\omega}^n[a,b]$. Some representations and other properties of this fractional derivative are proved. Some conclusions are presented.
DOI
10.3906/mat-1906-94
Keywords
$\omega$-weighted fractional derivatives and integrals, functional spaces, representations, absolutely continuous functions
First Page
662
Last Page
675
Recommended Citation
AKKURT, ABDULLAH; RESTREPO, JOEL ESTEBAN; and YILDIRIM, HÜSEYİN
(2020)
"Representations and properties of a new family of $\omega$-Caputofractional derivatives,"
Turkish Journal of Mathematics: Vol. 44:
No.
3, Article 4.
https://doi.org/10.3906/mat-1906-94
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss3/4
