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- Title
On Cauchy problems with Caputo Hadamard fractional derivatives.
- Authors
Adjabi, Y.; Jarad, F.; Baleanu, D.; Abdeljawad, T.
- Abstract
The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results.
- Subjects
CAUCHY problem; FIXED point theory; CAPUTO fractional derivatives; HADAMARD matrices; DIFFERENTIABLE functions
- Publication
Journal of Computational Analysis & Applications, 2016, Vol 21, Issue 1, p661
- ISSN
1521-1398
- Publication type
Article