Abstract degenerate fractional differential inclusions in Banach spaces

Kostić, Marko

doi:10.2298/aadm1701039k

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…in the space X := L p (Ω), where Ω is a bounded domain in R n , b > 0, m(x) ≥ 0 a.e. x ∈ Ω, m ∈ L ∞ (Ω), γ ∈ (0, 1) and 1 < p < ∞, as well as its semilinear analogue (Ω)∩H 2 (Ω), and A(x; D) is a second order linear differential operator on Ω with coefficients continuous on Ω and the Caputo fractional derivative D γ t is taken in a slightly weakened sense [35]; see [26, Example 6.1] and [38, Example 6.2] for more details.…”

Section: Set Alsomentioning

confidence: 99%

Generalized almost automorphic and generalized asymptotically almost automorphic solutions of abstract Volterra integro-differential inclusions

Kostić¹

2018

Fractional Differential Calculus

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In this paper, we analyze the existence and uniqueness of generalized weighted pseudo-almost automorphic solutions of abstract Volterra integro-differential inclusions in Banach spaces. The main results are devoted to the study of various types of weighted pseudo-almost periodic (automorphic) properties of convolution products. We illustrate our abstract results with some examples and possible applications.2010 Mathematics Subject Classification. 44A35, 42A75, 47D06, 34G25, 35R11. Key words and phrases. Weighted pseudo-almost periodicity, weighted pseudo-almost automorphy, convolution products, abstract Volterra integro-differential inclusions, multivalued linear operators.The author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia.where A(t) : D ⊆ X → X is a family of densely defined closed linear operators on a common domain D, independent of time t ∈ R, the history u t : (0, ∞] → X defined by u t (·) := u(t + ·) belongs to some abstract phase space B defined axiomatically, and f : R × B → X, g : R × B → X fulfill some conditions. Fractional calculus and fractional differential equations have received much attention recently due to its wide range of applications in various fields of science, such as mathematical physics, engineering, aerodynamics, biology, chemistry, economics etc (see e.g.[5], [24], [32]-[33] and [44]-[45]). In this paper, we essentially use only the Weyl-Liouville fractional derivatives (for more details, we refer the reader to the paper [42] by J. Mu, Y. Zhoa and L. Peng). The Weyl-Liouville fractional derivative D γ t,+ u(t) of order γ ∈ (0, 1) is defined for those continuous functions u : R → X such that t → t −∞ g 1−γ (t − s)u(s) ds, t ∈ R is a well-defined continuously differentiable mapping, by D γ t,+ u(t) := d dt t −∞ g 1−γ (t − s)u(s) ds, t ∈ R;

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Section: Set Alsomentioning

confidence: 99%

Generalized almost automorphic and generalized asymptotically almost automorphic solutions of abstract Volterra integro-differential inclusions

Kostić¹

2018

Fractional Differential Calculus

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“…During the peer-review process, the author has reconsidered and slightly improved the results of this paper for abstract degenerate fractional differential inclusions with multivalued linear operators satisfying the following condition (cf. [21] for more details):…”

Section: Semilinear Degenerate Cauchy Inclusionsmentioning

confidence: 99%

On a class of abstract degenerate fractional differential equations of parabolic type

Kostić¹

2018

Commentationes Mathematicae Universitatis Carolinae

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Strict Hölder regularity for fractional order abstract degenerate differential equations

Mansur

Dubey

2021

Ann. Funct. Anal.

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Abstract degenerate fractional differential inclusions in Banach spaces

Cited by 5 publications

References 16 publications

Generalized almost automorphic and generalized asymptotically almost automorphic solutions of abstract Volterra integro-differential inclusions

Generalized almost automorphic and generalized asymptotically almost automorphic solutions of abstract Volterra integro-differential inclusions

On a class of abstract degenerate fractional differential equations of parabolic type

Strict Hölder regularity for fractional order abstract degenerate differential equations

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