TY - JOUR
T1 - The modified fractional power series method for solving fractional undamped duffing equation with cubic nonlinearity
AU - Syam, Muhammed I.
N1 - Funding Information:
The authors would like to express their sincere appreciation to United Arab Emirates University for the financial support of Grant No.G00003060.
Publisher Copyright:
© 2020 InforMath Publishing Group/1562-8353 (print)/1813-7385 (online)/http://e-ndst.kiev.ua568
PY - 2020
Y1 - 2020
N2 - In this paper, the strongly nonlinear fractional undamped Duffing equation for undamped oscillators is studied. The physical and the mathematical model of nonlinear fractional Duffing equation for undamped oscillators is presented. The modified fractional power series (MFPS) method is employed to compute an approximation to the solution of this problem. The validity of the MFPS method is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existence of the solution is proved. In addition, the convergence of the proposed method is investigated.
AB - In this paper, the strongly nonlinear fractional undamped Duffing equation for undamped oscillators is studied. The physical and the mathematical model of nonlinear fractional Duffing equation for undamped oscillators is presented. The modified fractional power series (MFPS) method is employed to compute an approximation to the solution of this problem. The validity of the MFPS method is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existence of the solution is proved. In addition, the convergence of the proposed method is investigated.
KW - Fractional Duffing equation
KW - Modified fractional power series method
KW - Nonlinear boundary value problem
UR - http://www.scopus.com/inward/record.url?scp=85103003729&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85103003729&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85103003729
SN - 1562-8353
VL - 20
SP - 568
EP - 577
JO - Nonlinear Dynamics and Systems Theory
JF - Nonlinear Dynamics and Systems Theory
IS - 5
ER -