Asymptotic Behavior of Solutions to Nonlinear Fractional Differential Equations

• Main Authors: Mohammed D. Kassim, Khaled M. Furati, Nasser-Eddine Tatar
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2016-09-01
• Series: Mathematical Modelling and Analysis
• Subjects: asymptotic behavior; fractional differential equation; Riemann-Liouville fractional integral and fractional derivative
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/839

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.