10.1007/s40096-021-00453-x

Structures of exact solutions for the modified nonlinear Schrödinger equation in the sense of conformable fractional derivative

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  • Yeşim Sağlam Özkan*1,
  • Esra Ünal Yılmaz2,
  1. Department of Mathematics, Bursa Uludag University, Bursa, TR
  2. Department of Mathematics, Bolu Abant Izzet Baysal University, Bolu, TR

Published in Issue 2022-01-09

How to Cite

Sağlam Özkan, Y., & Ünal Yılmaz, E. (2022). Structures of exact solutions for the modified nonlinear Schrödinger equation in the sense of conformable fractional derivative. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00453-x
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Abstract

Abstract This paper is devoted to discuss analytically the conformable time-fractional modified nonlinear Schrödinger equation with the aid of efficient methods. The suggested model is a model used in ocean engineering to explain the propagation of water waves. At this stage, while using the proposed methods, the first step is to reduce the model defined by the conformable fractional derivative to the ordinary differential equation system with an appropriate transformation. We have obtained a variety of new families of exact traveling wave solutions including trigonometric, hyperbolic and exponential types. In related subject, the Adomian decomposition method is implemented to approximate the one of the solution of the underlying equation. For dynamic properties of the obtained solutions, we have depicted them graphically using computer programming to explain more efficiently the behavior of different shapes of solutions for the different values of free parameters with constraint conditions. Finally, a comparison is given for the solutions obtained in this study.

Keywords

  • Modified nonlinear Schrödinger equation,
  • Conformable fractional derivative,
  • Exact solutions

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