An extension of optimal auxiliary function method to fractional order high dimensional equations
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 pa...
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| Published in | Alexandria engineering journal Vol. 60; no. 5; pp. 4809 - 4818 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.10.2021
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1110-0168 2090-2670 |
| DOI | 10.1016/j.aej.2021.03.012 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Nawaz, Rashid Ahmad, Hijaz Nofal, Taher A. Ayaz, Muhammad Zada, Laiq Ullah, Farman Ahmad, Imtiaz |
| Author_xml | – sequence: 1 givenname: Rashid surname: Nawaz fullname: Nawaz, Rashid organization: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan – sequence: 2 givenname: Laiq surname: Zada fullname: Zada, Laiq organization: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan – sequence: 3 givenname: Farman surname: Ullah fullname: Ullah, Farman organization: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan – sequence: 4 givenname: Hijaz orcidid: 0000-0002-5438-5407 surname: Ahmad fullname: Ahmad, Hijaz email: hijaz555@gmail.com organization: Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan – sequence: 5 givenname: Muhammad surname: Ayaz fullname: Ayaz, Muhammad email: mayazmath@awkum.edu.pk organization: Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan – sequence: 6 givenname: Imtiaz surname: Ahmad fullname: Ahmad, Imtiaz email: imtiazkakakhil@gmail.com organization: Department of Mathematics, University of Swabi, Khyber Pakhtunkhwa, Pakistan – sequence: 7 givenname: Taher A. surname: Nofal fullname: Nofal, Taher A. email: t.a.hameed@tu.edu.sa organization: Department of Mathematic, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia |
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| Keywords | Fractional calculus and Otimal auxiliary function method Time fractional Zakharov-Kuznetsov equations Exact solutions |
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| SubjectTerms | and Otimal auxiliary function method Exact solutions Fractional calculus Time fractional Zakharov-Kuznetsov equations |
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| Title | An extension of optimal auxiliary function method to fractional order high dimensional equations |
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