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

被引：29
|
作者：
Kassim, M. D. [1 ]
Tatar, N. -E. [1 ]
机构：
[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia
来源：
ABSTRACT AND APPLIED ANALYSIS | 2013年
关键词：
EQUATIONS; SPACE;
D O I：
10.1155/2013/605029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页数：12
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