Weighted Integral Inequalities in Terms of Omega-Fractional Integro-Differentiation

Agarwal, Praveen; Jerbashian, Armen; Restrepo, Joel E.

doi:10.1007/978-981-13-3013-1_10

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ω -Weighted Fractional Integrals and Derivatives1

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2020

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“…The consideration of these weights ω will bring out more expected and unknown results. These kind of generalized fractional integrals and derivatives are partially studied in more general settings in [1,3,12,16,17] and the references therein.…”

Section: ω -Weighted Fractional Integrals and Derivativesmentioning

confidence: 99%

Representations and properties of a new family of ω-Caputo fractional derivatives

Akkurt¹,

Restrepo²,

Yıldırım³

2020

Turk J Math

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In the most general case of ω-weights, some normed functional spaces X p ω (a, b)(1 ≤ p ≤ ∞) , AC n 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 AC n γ,ω [a, b] are established. A general ω-weighted Caputo fractional derivative of order α is studied over AC n γ,ω [a, b]. Some representations and other properties of this fractional derivative are proved. Some conclusions are presented.

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