الفهرس 
Survey of the Main Mathematical ConceptsOnly 14 pages are availabe for public view
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Abstract
In this Thesis, we discuss how to use some modern computational techniques to construct analytical and approximate analytical solutions to initial value problems for linear and nonlinear differential equations with integer and fractional differentiation.In general, the nonlinear ordinary and partial differential equations have modeled nonlinear complicated phenomena and play an essential role in various scientific fields quantum mechanics, fluid mechanics, mathematical physics and engineering sciences. The process of finding the exact, analytical and approximate analytical solutions of the equations, gives better tools and help to understand and interoperate the considered phenomena.Also, the differential equations of fractional order, for generalized type of the classical differential equations of integer order. Recently, the fractional differential equations have been the focus of many researchers because of its frequent appearance in several applications in nuclear reactor dynamics, nuclear engineering and biomathematics. Therefore, considerable attention has been directed for solving fractional differential equations in quantum mechanics and biophysics. In addition, most nonlinear differential equations of fractional order do not have an exact analytic solution, so approximate analytical and numerical procedures such as the variational iterative method [36, 74], the homotopy perturbation method [9, 10, 75, 76] the Adomian decomposition method [77, 78], the residual power series method [33, 34], the differential termsform method [28], the integral iterative method [42-44], and Laplace transform [79] must be used. The Picard iteration method [17, 19] and the local fractional new iterative method [80] are relatively considered as modern techniques to provide an approximate analytical solutions to nonlinear initial value problems and they are particularly valuable as tools for researchers because they provide immediate and visible symbolic term of analytic and numerical approximate solutions for nonlinear differential equations without linearization or discretization.The application of the proposed pre-mentioned procedures will be extended for solving fractional differential equations.