|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
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