الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
In our Thesis, firstly in Chapter2 we implement OHAM to accurately solve the C-H equations. The accuracy of these results has been shown in the Tables (1-5) and they have been shown graphically in Figures (2.1-2.3) in order to highlight the efficiency and distinction of this method. The technique convergence is regulated by a flexible function known as the auxiliary function. The Caputo derivative fractional-order and the well-known least squares technique are used to determine the values of the unknown arbitrary constants in the auxiliary function. In the Caputo meaning, fractional-order derivatives are taken with results in the closed interval [0, 1]. The proposed technique is immediately applicable to Cahn-Hilliard equations, and no small or large parameter assumptions are required. Also, studies on this topic may lead to more interesting conclusions and results. Thus, it offers more realistic solutions on real physical problems. in chapter 3 we examined the approximated solutions of the fractional Cahn equation and Gardner equation by using LSRPS approach, which is combined with the RPSM and the least-squares approach. Approximate solutions with high accuracy with lower expansion terms have been given. Thus, we used data and figures to depict the approximate solutions. from the results obtained, we find that the present method provides convergent solutions with less processing and time than traditional RPSM and LRPSM in a simple way. Therefore, we support researchers using the LSRPS approach to obtain approximate solutions of other fractional differential equations. In the near future, we look forward to adding another method to RPSM to achieve a high-accuracy solution with lower expansion terms. we used the least square residual power series method to derive approximate solutions to time fractional Kawahara and Rosenau-Hynam equations based on caputo fractional derivation. The correctness of these results is displayed in Tables (1-2) and visually in Figures (4.1-4.6) to demonstrate the effectiveness and distinctiveness of this approach. It can be observed that the acquired solutions converge very quickly to the exact solutions, implying that the approximate solutions are quite close to the exact solutions. Furthermore, the examples provided here demonstrate that this technique converges faster than RPSM. It is demonstrates that the solutions found using the novel approach under investigation have a low error rate. In this regard, it is significant and a useful alternative approach for resolving nonlinear FDEs this is conclusion of chapter 4.finally in chapter 5Time-fractional Gas-Dynamic equations based on Caputo fractional derivation were approximated using the least Square Residual Power Series approach and the Optimal Homotopy Asymptotic method. At the same value of t and with the same number of approximations terms, the acquired solutions are found using the Least Square Residual Power Series Method (LSRPSM), see Table 2 and Figs. (5.4-5.6) which converges to the exact solutions more rapidly than the Optimal Homotopy Asymptotic Method (OHAM) sees Table 1 and Figs (5.1-5.3). This implies that the approximate solutions using LSRPSM technique are significantly closer to the exact solutions than the solutions using OHAM approach. According to the numerical results, the current approaches are simple, efficient, and provide extremely high precision for getting approximate solutions to various nonlinear fractional physical differential equations.