Asymptotic Behavior of Solutions to Nonlinear Fractional Differential Equations. Issue 5 (2nd September 2016)

• Record Type: Journal Article
• Authors: Kassim, Mohammed D.; Furati, Khaled M.; Tatar, Nasser-Eddine
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 5(2016)
• Page Start: 610
• Page End: 629
• Publication Date: 2016-09-02
• Subjects: asymptotic behavior -- fractional differential equation -- Riemann-Liouville fractional integral and fractional derivative; 34E10 -- 34A08 -- 26A33; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1198279
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: It is known that, under certain conditions, solutions of some ordinary differential equations of first, second or even higher order are asymptotic to polynomials as time goes to infinity. We generalize and extend some of the existing results to differential equations of non-integer order. Reasonable conditions and appropriate underlying spaces are determined ensuring that solutions of fractional differential equations with nonlinear right hand sides approach power type functions as time goes to infinity. The case of fractional differential problems with fractional damping is also considered. Our results are obtained by using generalized versions of GronwallBellman inequality and appropriate desingularization techniques.