Exploring solitary wave solutions in the Ivancevic option pricing model using a <i>ϕ</i> ⁶ -model fractional derivative technique

Abstract This study presents a ϕ 6 -model technique for the Ivancevic option pricing model (IOPM) in the sense of M-truncated fractional derivative to successfully derive traveling wave solutions. In addition to other new findings, periodic, dark, and bright topological solutions are found. To the best of our knowledge, this research has not been previously addressed in the literature. The work improves our comprehension of the model by revisiting the concept of solitary waves. Prior research has already employed a variety of techniques to derive analytical solutions, which has contributed to identify novel soliton solutions within this framework. To improve visualization, we also assign particular parameter values to generate 2D, 3D, and contour plots for some of the discovered solutions. By revealing significant information about the dynamics and patterns of the solutions, these illustrations help to clarify the behavior of the model. Furthermore, the effect of the fractional parameter on wave pattern propagation is also investigated. The outcomes show that our suggested approach is a useful mathematical tool for resolving non-linear evolution equations (NLEES) by producing fresh, more thorough solutions.

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