Adomian Decomposition Method For Solving Fractional Bratu-type Equations

Abstract

The Adomian decomposition method is proposed to solve fractional Bratu-type equations. The iteration procedure is based on a fractional Taylor series. Three examples are illustrated to show the presented method's efficiency and convenience.

RKM for solving Bratu-type differential equations of fractional order

“…To measure the accuracy of the method and comparison with Adomian's decomposition method (ADM) , we use the norm uniform as Example We consider the following Bratu‐type differential equation of fractional order The exact solution for α = 2 is u ( x ) =− 2 ln(cos( x )).…”

“…In this study, we wish to investigate the approximate solution of the following nonlinear fractional differential equation of Bratu‐type using reproducing kernel method (RKM) where is derivative operator of fractional order α , u ( x ) is unknown function on the interval [0,1] and C 1 , C 2 and λ are given constant . For α = 2, the problem has no, one or two solutions when λ > λ c o n s t , λ = λ c o n s t and λ < λ c o n s t , respectively, where λ c o n s t ≃3.513830719.…”

General solution of second order fractional differential equations

“…Due to this fact, finding an approximate solution of fractional differential equations is clearly an important task. In recent years, many effective methods have been proposed for the approximate solution fractional differential equations, such as Adomian decomposition method [3,4], homotopy perturbation method [5][6][7][8], homotopy analysis method [9,10], variational iteration method [11], generalized differential transform method [12] and other methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The organization of the paper is as follows: In Section 2, Basic definitions, such as conformable fractional derivative, and conformable fractional integral, will be presented.…”

Numerical solution for fractional Bratu’s initial value problem

“…Also, ADM was investigated for solving FBIVP in [7]. Babolian et al [8] presented reproducing kernel method (RKM) for solving FBIVP.…”