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

M. D. Kassim and N.-E. Tatar

Abstract and Applied Analysis, 2013, vol. 2013, 1-12

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:605029

DOI: 10.1155/2013/605029

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