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The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations. MSC 2010: 34A08, 26A33, 34K28, 35C10

A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense