Partial Differential Equations in Applied Mathematics (Dec 2022)
Analytical solution of fractional differential equations by Akbari–Ganji’s method
Abstract
According to the various and extensive applications of fractional calculus in a range of fields, such as engineering, biology, image processing, material science and economics, researchers have discovered new, simpler-to-use and more accurate approaches to solve these complicated problems today. In this article an analytical method called Akbari–Ganji’s method is proposed to solve nonlinear fractional differential equations. This method was used to solve nonlinear differential equations before but not fractional differential equations. In this method, first, the solution of the differential equation is considered as a polynomial with constant coefficients. Then, with the help of the initial conditions of the problem and also the Akbari–Ganji’s method’s boundary conditions, the final solution of the differential equation obtained by having the constant coefficients of the polynomial. The method was validated by comparing the answers of two nonlinear fractional differential equations to other methods. Some other examples also provided to confirm the strength and validity of the method.
