الفهرس 
1 A fractional Temimi-Ansari method with convergence analysis for solving KdV-Burgers and the BBMB equationsOnly 14 pages are availabe for public view
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Abstract
Fractional differential equations are used to model many phenomena in research and engineering, including solid-state physics, biology, optical fibers, fluid dynamics, nuclear physics, ecology, and quantum field theory. Fractional partial differential equations are dependent not only on the current time but also on the previous period’s history. In fractional order differential equations, a solution at a certain instance can only be obtained via prior values of the solution and its derivatives. The memory effect of the convolution increases the expressive power of the fractional integral equation. The essential concepts of fractional calculus, such as the Caputo and Atangana-Baleanu definitions, are provided in this thesis after a historical survey of the subject. The Temimi-Ansari method, a potent algorithm with applications in engineering, basic science, and applied mathematics, is generalized for solving fractional order linear and nonlinear partial differential equations. The analytical and approximate solutions of the nonlinear KdV-Burger’s equation and the nonlinear Benjamin-Bona-MahoneyBurger equation of time-fractional order have been discussed and developed using the Temimi-Ansari method. The above equations, which include both dispersion and damping, have been categorized as typical equations for a large class of nonlinear systems under weak approximations of nonlinearity and wavelength. The novelty of the thesis appears in the widespread use of the Caputo fractional operator to solve ordinary differential equations with exceptionally accurate results using both known series solutions and more intricate nonlinear solutions. Additionally, it does not require any assumptions for nonlinear terms. Both tables and graphs are used to show the numerical results for various cases of the equations. The convergence analysis for the present approach was successfully completed. The approach is convenient and effective for solving nonlinear fractional equations and is extremely capable of minimizing the size of the analytical steps. In contrast, Fisher provided a differential equation gene selection model that is about populations, which can be tumor cells, people, or fish. Fisher’s equation describes the wave of beneficial genes advancing. This equation piques the interest of scholars due to its different applications in science and engineering. The same equation appears in the Brownian motion process, autocatalytic chemical reactions, neurophysiology, flame propagation, and nuclear reactor theory. The Temimi-Ansari method was successfully used to provide the analytical solutions to the nonlinear Fisher’s equation with time-fractional order. In light of the Laplace substitution method, this powerful algorithm is generalized for solving linear and nonlinear partial differential equations of fractional order. We present new approximate solutions to some linear and nonlinear fractional partial differential equations, which include mixed partial derivatives using Laplace substitution method. This method is entirely based on the wellknown Laplace transform and Adomian polynomial. Looking at several studies, we find that the results obtained from this technique converge well with the exact solutions. Coronavirus infection (COVID-19) is a considerably dangerous disease with a high demise rate around the world. One of the most effective strategies for comprehending and controlling the spread of this epidemic is to model it using a powerful mathematical model. However, mathematical modeling with a fractional operator can provide explanations for the possibility and gravity of this disease. Accordingly, basic information will be provided to identify the kind of measure and intrusion that will be required to control the spread of the disease. In this thesis, a new dynamic study of the fractional novel coronavirus (2019-nCOV) pandemic (SEAIRV model) with data from Ghana using the fractional Temimi-Ansari method is described. The power series solution is determined using the derivatives of the Caputo and Atangana Baleanu with the Caputo sense. The generated results are illustrated with figures that show the expected system behavior. The efficiency and accuracy of this technique are demonstrated by the existence and uniqueness of solutions. The results show that the scheme used is very accurate and easy to use for solving nonlinear fractional differential equations models. In sensitivity analysis, it was determined that R0 increases with some parameters and decreases with other parameters. This means that to reduce disease prevalence, those parameters with negative rates of the fractional derivative must be reduced in the environment. Besides, we suggest modeling the Coronavirus pandemic by the SEIARPQ model of fractional order with Caputo sense which didn’t show up in the literature previously. The stability analysis, existence, uniqueness theorems, and numerical solutions of such models are displayed. The current research can affirm the applicability and impact of fractional operators on true issues. All results are numerically simulated using MATLAB programming.