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On Asymptotics of Some Fractional Differential Equations

    Lukasz Plociniczak Affiliation

Abstract

In this paper we study the large-argument asymptotic behaviour of certain fractional differential equations with Caputo derivatives. We obtain exponential and algebraic asymptotic solutions. The latter, decaying asymptotics differ significantly from the integer-order derivative equations. We verify our theorems numerically and find that our formulas are accurate even for small values of the argument. We analyze the zeros of fractional oscillations and find the approximate formulas for their distribution. Our methods can be used in studying many other fractional equations.

Keyword : approximation, numerical method, asymptotic solution

How to Cite
Plociniczak, L. (2013). On Asymptotics of Some Fractional Differential Equations. Mathematical Modelling and Analysis, 18(3), 358-373. https://doi.org/10.3846/13926292.2013.804888
Published in Issue
Jun 1, 2013
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This work is licensed under a Creative Commons Attribution 4.0 International License.