University of Khartoum

A New Technique of Laplace Variational Iteration Method for Fractional Differential Equations

A New Technique of Laplace Variational Iteration Method for Fractional Differential Equations

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Title: A New Technique of Laplace Variational Iteration Method for Fractional Differential Equations
Author: Elawad, Fatma Ahmed
Abstract: The objective of this research is to investigate the solutions of fractional linear and nonlinear differential equations. Many analytical methods, as Laplace and Fourier transform besides the semi-analytical methods, as variational iteration and differential transform followed in deriving the solutions. The fractional derivatives are described in the Caputo sense. A new method to solve the fractional differential equations is proposed, which combines the two methods – the Laplace transform and variational iteration. This method is named ''A New Technique of Laplace Variational Iteration Method''. This new technique is used to overcome the difficulties arising in identifying the general Lagrange multiplier in the method of variational iteration. To demonstrate this new algorithm, various types of fractional problems are successively solved. Moreover, this technique is focused in finding the exact solutions of space-time fractional telegraph equations where the obtained solutions are expressed in a compact form in terms of Mittage-Leffler functions. As special cases, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders. Finally, the differential transform method is applied to prove the symmetry of fractional telegraph equation.
Description: 122page
URI: http://khartoumspace.uofk.edu/123456789/22603


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