Modified Variation Iteration method for fraction space- time partial differential heat and wave equations

Abstract: Variational iteration method (VIM) has been favorably applied to various kinds of differential equations. The main property of the method is in its ?exibility and ability to solve differential equations accurately and conveniently. Recent trends and developments in the use of the method will be reviewed. The equations arising in various engineering applications will be surveyed. The con?uence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly differential equations which cannot be successfully dealt with by classical methods. (VIM) is uniquely quali?ed to address this challenge. The ?exibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions. This paper outlines the basic conceptual framework of (VIM) with application to fractional order, space and time, partial differential equations, wave and heat with integral term, these kind of equations, with steps to finding multiply Lagrange and three methods to choose the start solution ( zeros solution), are discussed. Different examples will be solved and those figures will be given to show what happen to the equations with different fractional order. Matalab program was used to find these figures.

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[I. K. Youssef , A. M. Shukur (2014); Modified Variation Iteration method for fraction space- time partial differential heat and wave equations Int. J. of Adv. Res. 2 (2). 0] (ISSN 2320-5407). www.journalijar.com

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