Journal of Applied Nonlinear Dynamics
On the Asymptotic Stability Behaviours of Solutions of Nonlinear Differential Equations with Multiple Variable Advanced Arguments
Journal of Environmental Accounting and Management 8(2) (2019) 239249  DOI:10.5890/JAND.2019.06.007
Emel Biçer$^{1}$, Cemil Tunç$^{2}$
$^{1}$ Department of Mathematics, Faculty of Arts and Sciences, Bingol University, 12000 Bingol, Turkey
$^{2}$ Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey
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Abstract
We pay our attention to a nonlinear differential equation of first order with multiple two variable advanced arguments. We find sufficient conditions satisfying the convergence (C) and exponential convergence (EC) of solutions of the considered nonlinear advanced differential equation (NADE) by contraction mapping principle (CMP). The obtained results improve and extend the results can be found in the relevant literature from a case of linear advanced differential equation (LADE) of first order to a case of (NADE) of first order with multiple two variable advanced arguments. We give examples for illustrations by applying MATLABSimulink. It is also clearly shown the behaviors of the orbits for the special cases of the considered (NADE).
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