Special Session 108: New Trends in Fractional Modelling with General Kernel
Generalization of 1D-Asymmetric Harmonic Oscillator Model via Different Kernels
Ozlem Defterli
Associate Professor Dr., Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara Turkey
Co-Author(s): Dumitru Baleanu,Amin Jajarmi, Ozlem Defterli, Noorhan Alshaikh, Jihad Asad
Abstract:
The fractional dynamics of a one-dimensional asymmetric harmonic oscillator model having quadratic nonlinearity is investigated within a generalized kernel. Using the principles of the calculus of variations, a system of two-coupled fractional differential equations with a nonlinear component is derived as fractional Euler-Lagrange equations of the corresponding system. The numerical solution to the system is evaluated and then simulated concerning various model parameter values, including mass, linear and quadratic nonlinear stiffness, and the order of the fractional derivative.