Authors: Atanacković, Teodor
Janev, Marko 
Pilipović, Stevan
Zorica, Dušan 
Title: Convergence analysis of a numerical scheme for two classes of non-linear fractional differential equations
Journal: Applied Mathematics and Computation
Volume: 243
First page: 611
Last page: 623
Issue Date: 15-Sep-2014
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2014.06.047
Abstract: 
We use the expansion formula for the fractional derivatives to reduce the problem of solving non-linear fractional order differential equations arising in mechanics to the problem of solving a system of integer order differential equations. We prove the convergence of the solutions to the reduced integer order systems to the solutions of the original problem. The procedure is illustrated by two specific examples.
Keywords: Expansion formula | Gronwall inequality | Non-linear fractional differential equations
Publisher: Elsevier
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Integrated system for detection and estimation of fire development by real-time monitoring of critical parameters 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Development of Dialogue Systems for Serbian and Other South Slavic Languages 

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