Well-Posedness and Stability for a Differential Problem with Hilfer-Hadamard Fractional Derivative | Zendy

Mohammed D. Kassim | Zendy; Nassereddine Tatar | Zendy

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Well-Posedness and Stability for a Differential Problem with Hilfer-Hadamard Fractional Derivative

Author(s) -

Mohammed D. Kassim,

Nassereddine Tatar

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/605029

Subject(s) - generalizations of the derivative , mathematics , fractional calculus , derivative (finance) , hadamard transform , equivalence (formal languages) , mathematical analysis , fréchet derivative , type (biology) , cauchy problem , differential equation , initial value problem , pure mathematics , banach space , ecology , biology , financial economics , economics

Motivated by the Hilfer fractional derivative (which interpolates the Riemann-Liouville derivative and the Caputo derivative), we consider a new type of fractional derivative (which interpolates the Hadamard derivative and its Caputo counterpart). We prove the well-posedness for a basic Cauchy type fractional differential equation involving this kind of derivative. This is established in an appropriate underlying space after proving the equivalence of this problem with a certain corresponding Volterra integral equation.

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