(7)Analytic solutions of the generalized water wave dynamical equations based on time-space symmetric differential operator
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Rabha W. Ibrahima,∗ , Chandrashekhar Meshramb, Samir B. Hadidc , Shaher Momanic,d
aCloud Computing Center, University Malaya, Malaysia
b Department of Mathematics and Computer Science, Rani Durgavati University, Jabalpur, India
c Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, UAE
d Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan
Received 10 October 2019; received in revised form 6 November 2019; accepted 6 November 2019
Available online 12 November 2019
Abstract
It is well known that there is a deep connection between the symmetric and traveling wave solutions. It has been shown that all symmetric
waves are traveling waves. In this paper, we establish new analytic solution collections of nonlinear conformable time-fractional water wave
dynamical equation in a complex domain. For this purpose, we construct a new definition of a symmetric conformable differential operator
(SCDO). The operator has a symmetric representation in the open unit disk. By using SCDO, we generalize a class of water wave dynamical
equation type time-space fractional complex Ginzburg–Landau equation. The results show that the obtainable approaches are powerful,
dependable and prepared to apply to all classes of complex differential equations.
© 2020 Published by Elsevier B.V. on behalf of Shanghai Jiaotong University.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Analytic solution; Conformable calculus; Fractional calculus; Water wave equations; Majorization; Subordination and superordination.