Electron. J. Diff. Equ., Vol. 2016 (2016), No. 207, pp. 1-14.

Existence and continuation of solutions for Caputo type fractional differential equations

Changpin Li, Shahzad Sarwar

Abstract:
In this article, we consider a fractional differential equation (FDE) with Caputo derivative and study the existence and continuation of its solution. Firstly, we prove a theorem on the existence of local solutions. Then we extend the continuation theorems for ODEs to those FDEs. Also several global existence results for FDE are obtained.

Submitted April 11, 2016. Published August 01, 2016.
Math Subject Classifications: 34A08, 35A01.
Key Words: Fractional differential equation; Caputo derivative; local solution; continuation theorem; global solution.

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Changpin Li
Department of Mathematics
Shanghai University
Shanghai 200444, China
email: lcp@shu.edu.cn
Shahzad Sarwar
Department of Mathematics
Shanghai University
Shanghai 200444, China
email: shahzadppn@gmail.com

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