Abstract
Fractional Phi-4 equation plays a crucial role in many studies of nuclear and particle physics. In this paper, the fractional Phi-4 equation is studied for two recently developed definitions of fractional derivatives and the comparison of the results with both derivatives is presented. The wave solutions of fractional Phi-4 equation are obtained using the extended \(\sinh\)-Gordon equation expansion method. The beta and M-truncated fractional effects are considered. New complex trigonometric and complex hyperbolic function solutions are retrieved. Dark solitons and periodic solitary waves are observed for obtained solutions. The wave profiles obtained for the beta and M-truncated derivatives are compared for different values of fractional order using graphical simulations. The presented results are novel and the extended sinh-Gordon equation expansion method has been utilized to investigate fractional Phi-4 equation with beta and M-truncated derivative for the first time in this work.
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GA participated in the conceptualization, data curation, investigation, methodology, software implementation, validation, visualization and writing the original draft. SA participated in the conceptualization, administration, validation, visualization and writing of the manuscript. MS participated in the formal analysis, investigation, supervision, review and editing of the manuscript. MM participated in the data curation, formal analysis, software and writing of the original draft. All authors read and approved the final manuscript.
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Akram, G., Arshed, S., Sadaf, M. et al. Comparison of fractional effects for Phi-4 equation using beta and M-truncated derivatives. Opt Quant Electron 55, 282 (2023). https://doi.org/10.1007/s11082-023-04549-7
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DOI: https://doi.org/10.1007/s11082-023-04549-7