الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
In this work, some space-time fractional equations that describe phenomena in physics have been derived. This has been carried out as follows: The semi-inverse method is used to evaluate the Euler-Lagrange equation in its regular form. Then the variational technique of Agrawal is used to derive the space-time fractional form of the evolution equation. This technique is applied here to derive the Burger, Korteweg-de Vries (KdV), Korteweg-de Vries-Burger (KdV-Burger), and Kadomtsev-Petviashvili (KP) equations. In addition, they have been solved these space –time fractional employing the fractional sub-equation method.
Moreover, Euler-Lagrange equations are used to investigate real problems.
Firstly, the propagation of the pressure wave in a fluid filled elastic tube has been studied. The reductive perturbation method is used to derive KdV equation. Then, the space-time fractional KdV is formulated using Euler-Lagrange variational technique and is solved by fractional sub-equation method. The effect of the space time fractional parameter on the propagation of pressure waves has been investigated for a fluid filled elastic tube.
Secondly, the KdV-Burger equation is derived by the reductive perturbation method for dust acoustic waves in un-magnetized dusty plasma having electrons, singly charged non-thermal ions, hot and cold dust species. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. Then, the formulation and solution of space-time-fractional KdV-Burgers equation has been achieved Also; the effect of space-time fractional parameter on the behavior of the dust acoustic waves in the dusty plasma has been investigated.
Finally, the KP equation in un-magnetized plasma having ions and super-thermal electrons and positrons is formulated. Also, the formulation and solution of space-time fractional KP equation has been obtained. Also, the effects of space-time fractional order and the super-thermal parameter on the properties of obtained soliton have been investigated.