This article presents the approximate analytical solutions of first order linear partial differential equations (PDEs) with fractional time- and space- derivatives. With the aid of initial values, the explicit solutions of the equations are solved making use of reliable algorithm like homotopy analysis method (HAM). The speed of convergence of the method is based on a rapidly convergent series with easily computable components. The fractional derivatives are described in Caputo sense. Numerical results show that the HAM is easy to implement and accurate when applied to space- time- fractional PDEs.
Das, Subir,; Kumar, R.; Gupta, P. K.; and Jafari, Hossein
Approximate Analytical Solutions for Fractional Space- and Time- Partial Differential Equations using Homotopy Analysis Method,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 5,
2, Article 22.
Available at: https://digitalcommons.pvamu.edu/aam/vol5/iss2/22