An extension of optimal auxiliary function method to fractional order high dimensional equations

• Published in: Alexandria engineering journal Vol. 60; no. 5; pp. 4809 - 4818
• Main Authors: Nawaz, Rashid, Zada, Laiq, Ullah, Farman, Ahmad, Hijaz, Ayaz, Muhammad, Ahmad, Imtiaz, Nofal, Taher A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2021; Elsevier
• Subjects: and Otimal auxiliary function method; Exact solutions; Fractional calculus; Time fractional Zakharov-Kuznetsov equations; Fractional calculus; and Otimal auxiliary function method; Time fractional Zakharov-Kuznetsov equations; Exact solutions
• ISSN: 1110-0168; 2090-2670
• DOI: 10.1016/j.aej.2021.03.012

In this article, the new approach called, the optimal auxiliary function method (OAFM) has been extended with the help of the fractional complex transform method (FCTM) to fractional order partial differential equations (PDEs). The beauty of the method is that, there is no need for small or large parameter assumption in the problem. Similarly, the proposed method gives an approximate solution after only one itearion. To test the proposed method, we take the time-fractional order Zakharov-Kuznetsov equations as a test example. The computed results of the suggested method are compared with the new iterative method (NIM), perturbation iteration method (PIA), and Residual power series method (RPSM). The accuracy and effectiveness of the proposed method can be proven by numerical and graphical results.