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In this paper, we introduce the q -Shehu transform. Further, we define the generalized hyper-Bessel function. Also, we state the q -Shehu transform for some elementary functions. The present aim in this paper is to obtain the solutions of the q -fractional kinetic equations in terms of the established generalized hyper-Bessel function by applying the established q -Shehu transform. Also, we give some special cases of our main results. At the end of this paper, we give the numerical values and the graphical representations of these solutions by using the software MATLAB. [ABSTRACT FROM AUTHOR]

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations. [ABSTRACT FROM AUTHOR]