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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Analytical Solutions of some Fractional Order Nonlinear Evolution Equations by Sine-Cosine Method

Discontinuity, Nonlinearity, and Complexity 12(2) (2023) 275--286 | DOI:10.5890/DNC.2023.06.004

Department of Physics, Veer Surendra Sai University of Technology, Odisha-768018, India

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In our recent work, we study three fractional order nonlinear evolution equations by sine-cosine method, a class of traveling wave solutions with significant physical structures are obtained. The solutions include periodic solutions, soliton solutions, bell shaped solutions with the estimated values of involved parameters. The significance of contemplating and applying such equations originates from a dynamical point of view of the complexities of non linear physical models. Some real time problems of nonlinear physical worlds can be realized such as fractional Zoomeran equation helps to understand time evolution of single scalar field and novelty of boomerons and trappons, numerous wave phenomenas in solid state physics, plasma physics and quantum filed theory can be understood by fractional Hirota-Ramani equation and fractional Zarkhov-Kuznetsov-Benjamin-Bona-Mohany equation helps to understand the propagation of long range gravity waves in fluid mechanics and waves in plasma. The importance of trigonometric and hyperbolic solution in fractional calculus discussed. By the implementation of MATLAB graphical plots are shown.


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