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    On Finite Part Integrals and Hadamard-Type Fractional Derivatives

    Source: Journal of Computational and Nonlinear Dynamics:;2018:;volume( 013 ):;issue: 009::page 90905
    Author:
    Ma, Li
    ,
    Li, Changpin
    DOI: 10.1115/1.4037930
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.
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      On Finite Part Integrals and Hadamard-Type Fractional Derivatives

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    contributor authorMa, Li
    contributor authorLi, Changpin
    date accessioned2019-02-28T11:11:54Z
    date available2019-02-28T11:11:54Z
    date copyright7/26/2018 12:00:00 AM
    date issued2018
    identifier issn1555-1415
    identifier othercnd_013_09_090905.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4253727
    description abstractThis paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleOn Finite Part Integrals and Hadamard-Type Fractional Derivatives
    typeJournal Paper
    journal volume13
    journal issue9
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.4037930
    journal fristpage90905
    journal lastpage090905-7
    treeJournal of Computational and Nonlinear Dynamics:;2018:;volume( 013 ):;issue: 009
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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