A Comparative Study for Solving Nonlinear Fractional Heat -Like Equations via Elzaki Transform
Mohand M. Abdelrahim Mahgoub *
Department of Mathematics, Faculty of Science and Technology, Omdurman Islamic University, Khartoum, Sudan and Department of Mathematics, Faculty of Sciences and Arts-Almikwah, Albaha University, Saudi Arabia.
Abdelilah K. Hassan Sedeeg
Department of Mathematics, Faculty of Sciences and Arts-Almikwah, Albaha University, Saudi Arabia and Department of Mathematics, Faculty of Education, Holy Quran and Islamic Sciences University, Khartoum, Sudan.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the Homotopy Perturbation Elzaki Transform Method (HPETM) and Homotopy Decomposition Method (HDM) are used to solve nonlinear fractional Heat - Like equations. Both methods are very efficient techniques and quite capable, practically for solving different kinds of linear and nonlinear fractional differential equations .The results reveal that the (HDM) has an advantage over the (HPETM) which is that it solves the nonlinear problems using only the inverse operator which is basically the fractional integral. Additionally there is no need to use any other inverse transform to find the components of the series solutions as in the case of HPETM. As a consequence the calculations involved in HDM are very simple and easy execution.
Keywords: Homotopy decomposition method, integral transforms, nonlinear Heat -Like equation, Elzaki transform