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The modified exponential function method is used to obtain some new analytical solutions of the nonlinear Gerdjikov–Ivanov equation with the M-fractional operator. The novel obtained solutions are expressed in hyperbolic, trigonometric, and exponential function forms. Moreover, the instability modulation and gain spectra of the Gerdjikov–Ivanov equation are also analyzed. Constraints conditions are utilized to verify the existence of the solutions. Presented solutions are novel, satisfy and verify the M-fractional Gerdjikov–Ivanov equation. [ABSTRACT FROM AUTHOR]

The modified exp - Ω ζ -expansion function method is applied to the Wu–Zhang system with conformable time-fractional derivative to construct new analytical solutions. We have obtained some soliton-type solutions such as dark, singular and combined soliton solutions. We have seen that all solutions have provided the mentioned equation system. For the suitable value of the solutions, the 2D–3D and contour surfaces have been plotted. [ABSTRACT FROM AUTHOR]

In the present investigation, the q-homotopy analysis transform method (q-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas. Numerical simulation has been conducted to prove that the proposed technique is reliable and accurate, and the outcomes are revealed using plots and tables. The comparison between the obtained solutions and the exact solutions shows that the proposed method is efficient and effective in solving nonlinear complex problems. Moreover, the proposed algorithm controls and manipulates the obtained series solution in a huge acceptable region in an extreme manner and it provides us a simple procedure to control and adjust the convergence region of the series solution. [ABSTRACT FROM AUTHOR]