Open AccessON ASYMPTOTICS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS
Author(s) -
Łukasz Płociniczak
Publication year - 2013
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2013.804888
Subject(s) - mathematics , fractional calculus , argument (complex analysis) , integer (computer science) , exponential function , order (exchange) , algebraic number , differential equation , distribution (mathematics) , mathematical analysis , biochemistry , chemistry , finance , computer science , economics , programming language
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.