APPROXIMATE SOLUTIONS OF FPDES WITH FRACTIONAL DERIVATIVE OF ANTAGANA-BALEANU IN CAPUTO SENSE

Mohammed AbdulShareef Hussein; Shurooq Kamel Abd

Mohammed AbdulShareef Hussein Education Directorate of Thi-Qar, Ministry of Education, Thi-Qar, Iraq Scientific Research Center, Alayen University, Nasiriyah, Iraq
Shurooq Kamel Abd Department of mathematics, College of Computer Science and mathematics, Thi Qar University, Nasiriyah, Iraq

Keywords: Natural Transform, Homotopy Permutation Method, Atangana-Baleanu Operator, Variational Iteration Method.

Abstract

The natural variational iteration technique (NVIM) and the natural homotopy permutation method (NHPM) are described in this article to provide an approximation solution to fractional differential equations using the fractional derivative of Atangana Baleaneau in Caputo sense. The algorithms of the two ways were compared, and the results of the two methods were shown to be successful for obtaining the approximate solution for this sort of fractional differential equation.

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