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Fractional Abstract Differential Equations and Applications

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Abstract

Boundary value problems for fractional elliptic equations with parameter in Banach spaces are studied. Uniform \(L_{p}\)-separability properties and sharp resolvent estimates are obtained for elliptic equations in terms of fractional derivatives. Particularly, it is proven that the fractional elliptic operators generated by these equations are positive and also are generators of the analytic semigroups. Moreover, maximal regularity properties of the fractional abstract parabolic equation are established. As an application, the parameter-dependent anisotropic fractional differential equations and the system of fractional differential equations are studied.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Istanbul Okan University, Akfirat, Tuzla, Istanbul, 34959, Turkey

    Veli Shakhmurov

  2. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, F. Agaev 9, 1141, Baku, Azerbaijan

    Veli Shakhmurov

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  1. Veli Shakhmurov
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Correspondence to Veli Shakhmurov.

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Communicated by Fuad Kittaneh.

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Shakhmurov, V. Fractional Abstract Differential Equations and Applications. Bull. Malays. Math. Sci. Soc. 44, 1065–1078 (2021). https://doi.org/10.1007/s40840-020-00977-w

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  • DOI: https://doi.org/10.1007/s40840-020-00977-w

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