A semi-analytic method to solve nonlinear differential equations with arbitrary order

Abstract

In this paper, we describe the new Adomian Decomposition General Transform Method (ADGTM). Further, the efficacy of the method is proved by applying it to well-known equations, such as the logistic equation, Emden–Lane–Fowler equation, Gardner equation, and Cahn–Hilliard equation, in fractional order to study the intrinsic behavior. We compare the results with other well-known methods like RPSM, and q-HATM to prove the reliability and accuracy of the proposed method. For the selected applications, we frame 2D and 3D graphs to explain how the fractional-order derivative affects the behavior of the obtained solutions.

Keywords

• General transform method
• Fractional differential equations
• Adomian Decomposition Method
• Fractional ordinary differential equations
• Fractional partial differential equations