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In this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order α. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required α -corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when α = 1. [ABSTRACT FROM AUTHOR]

In this paper, new analytical obliquely propagating wave solutions for the time fractional extended Zakharov–Kuzetsov (FEZK) equation of conformable derivative are investigated. By using the main properties of the conformable derivative, the FEZK equation is transformed into integer-order differential equations, and the reduced equations are solved via the generalized exponential rational function method (GERFM). The shape and features for the resulting solutions are illustrated through three-dimensional (3D) plots and corresponding contour plots for various values of the free parameters. [ABSTRACT FROM AUTHOR]

The O(3) nonlinear sigma model is investigated using multi-Hamilton-Jacobi formalism. The integrability conditions are investigated and the results are in agreement with those obtained by Dirac's method. By choosing an adequate extension of phase space we describe the transformed system by a set of three Hamilton-Jacobi equations and calculate the corresponding action. [ABSTRACT FROM AUTHOR]

The solution of the Lax tensor equations in the case L[sub αβγ]= -L[sub βαγ] was analyzed. The Lax tensors on the dual metrics were investigated. We classified all two-dimensional metrics having the symmetric Lax tensor L[sub αβγ]. The Lax tensors of the flat space, Rindler system and its dual were found. [ABSTRACT FROM AUTHOR]