Document Type

Article

Publication Date

2018

Publication Source

Journal of Fractional Calculus and Applications

Abstract

Let n ≥ 1 denote an integer and let n - 1 < α ≤ n: We consider an initial value problem for a nonlinear Caputo fractional differential equation of order α and obtain results analogous to well known results for initial value problems for ordinary differential equations. These results include Picard’s existence and uniqueness theorem, Peano’s existence theorem, extendibility of solutions to the right, maximal intervals of existence, a Kamke type convergence theorem, and the continuous dependence of solutions on parameters. The nonlinear term is assumed to depend on higher order derivatives and solutions are obtained in the space of n - 1 times continuously differentiable functions.

Inclusive pages

178-195

ISBN/ISSN

2090-584X

Document Version

Published Version

Comments

This document is made available in compliance with the publisher's policy on self-archiving or with the express permission of the publisher. Permission documentation is on file.

Volume

9

Issue

2

Peer Reviewed

yes

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Mathematics Commons

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