One Solution of Multi-term Fractional Differential Equations by Adomian Decomposition Method: Scientific Explanation

Abstract

The Adomian decomposition method (ADM) is applied to solve the of nonlinear multi-term fractional differential equations of the Form \(D_{*}^\alpha\)Y(X) = \(\textstyle \sum_{i=0}^n\)\(a_i\)(x)\(\textstyle D_{*}^{\beta_i}\) Y(X) + \(a_0\) (x)y(x) + N ((x, y(x), \(D_{*}^{\beta_1}\)Y(X), ..., \(D_{*}^{\beta_n}\)Y(X)) + g (x) under the initial conditions \(y^{(i)}(0)=c_i\) (0 \(\le\) i \(\le\) m -1) where N is nonlinear function of x,y(x), \(D_{*}^{\beta_1}\)Y(X), ... ..., \(D_{*}^{\beta_n}\)Y(X) and g(x) and a_i(x) are functions of x. Also \(\alpha\) > \(\beta_n\)> …… \(\beta_1\) > 0, (m -1 <\(\alpha\) \(\le m,\ and \ m\in N)\) . Some examples of the solution are also presented for better comprehension.