Fractional order Like-Parabolic and Like-Hyperbolic by He\'s method

This paper talks about Fractional order partial differential equations that considered as one of the recent subjects although the concepts of fractional calculus are old as the beginning of classical calculus with Newton\'s and Leibentz. The importance of fractional calculus which proved almost all partial differential equations with fractional order and given the best description to problems in different science. Also, the fractional calculus (derivatives and integral) definitions will be given in this paper as the basis which is using to solve problems. The paper in general considers some of models of the main categories where fractional order Like-Parabolic and Like-hyperbolic Partial differential Equations (FPDE\'s) in one-dimensional will be solved by using He\'s numerical method. The He\'s method has accurate and easily to solve many problems. The flexibility and ability of the suggested method to solve different fractional order partial differential problems is illustrated in the present work. He\'s numerical method has importance in Fractional Calculus, because, it gives a semi analytic solutions for the both linear and nonlinear partial differential equations without more conditions. The using of He\'s method doesn’t need presence of the small-parameters in the PDE’s; also, it doesn’t need the nonlinearity for the dependent variable and its derivatives. The mathematical researchers, sometime, called this method “a modification of the general Lagrange multiplier method”. He\'s puts this method as a simple and general method to providing an approximation solution to different fractional order differential equations as an iterative sequence to find the final solutions. Different examples will be solved to show the powerful of He’s numerical method. Python programs used to solve problems and showing the different between analysis and approximation solutions at different fractional orders. Finally the conclusion of results will be given.