Abdullah AKKURT, Joel Esteban RESTREPO, Hüseyin YILDIRIM

Representations and properties of a new family of $\omega$-Caputo fractional derivatives

Öz In the most general case of ω-weights, some normed functional spaces X p ω a, b 1 ≤ p ≤ ∞ , ACn γ,ω[a, b] and a generalization of the fractional integro-differentiation operator are introduced and analyzed. The boundedness of the ω-weighted fractional operator over X p ω a, b is proved. Some theorems and lemmas on the properties of the invertions of the mentioned operator and several representations of functions from ACn γ,ω[a, b] are established. A general ω-weighted Caputo fractional derivative of order α is studied over ACn γ,ω[a, b]. Some representations and other properties of this fractional derivative are proved. Some conclusions are presented.

Anahtar Kelimeler:

ω-weighted fractional derivatives and integrals, functional spaces, representations, absolutely continuous functions

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