Existence and Uniqueness of the Solution to a Nonlinear Differential Equation with Caputo Fractional Derivative in the Space of Continuously Differentiable Functions

2012/08/10 by Sunae Pak, Pak, Sunae, Myongha Kim +1
Mathematics · Physics and Astronomy · #26A33 #34A08 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #msc:26A33 #msc:34A08

paper · pdf · doi:10.48550/arxiv.1208.2107

9 pages, in version 2 added references and divided into sections with subtiltles and revised main text

arxiv created 2013/04/08 · arxiv updated 2013/09/27

Abstract

In the paper, we considered the existence and uniqueness of the global solution in the space of continuously differentiable functions for a nonlinear differential equation with the Caputo fractional derivative of general form. Our main method is to derive an integral equation corresponding to the original nonlinear fractional differential equation and to prove their eqivalence. Once we prove the equivalence, then the proof of existence and uniquness of solution can be done by standard way of using Banach fixed point theorem.

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