Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

Recently, a new definition of fractional derivative called as the conformable fractional derivative which based on limits introduced by Khalil et al (2014). Later, Abdeljawad (2015) improved these definitions and gave the basic concepts in this new fractional calculus. In this paper, we generalize Abel's formula and Wronskian determinant definition and establish existence and uniqueness theorems for sequential linear conformable fractional differential equations.

Güngör, Nihan; Sağir, Birsen

Let 1≤q, p < ∞ and υ,w be Beurling's weight functions on Rd. In this article we deal with harmonic properties of intersection space Aq,pk,υ,w (Rd) = Lqυ (Rd) ∩ Wp,wk (Rd) defined by aid of weighted Lebesgue space Lqυ (Rd) and weighted Sobolev space Wp,wk (Rd). We research the inclusions and inequalities between the spaces Aq,pk,υ,w (Ω) where Ω ⊂ Rd be an open set. Finally, we proved that the spaces M (A1,pk,w (Rd), L1w (Rd)) can be identified with the weighted spaces of bounded measures Mw (Rd).