Homotopy analysis method for solving fractional hyperbolic partial differential equations

Abstract

In the present paper, the solutions of the hyperbolic partial differential equation with fractional time derivative of order α(1<α≤2) are obtained with the help of approximate analytical method of nonlinear problems called the homotopy analysis method. By using initial values, the explicit solutions of the equations for different particular cases have been derived which demonstrate the effectiveness, validity, potentiality and reliability of the method in reality. Numerical results for different particular cases are presented graphically. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. © 2011 Taylor & Francis.