This manuscript is devoted to consider Natural transform (NT) coupled with homotopy perturbation method (HPM) for obtaining series solutions to some linear and nonlinear fractional partial differential equations (FPDEs). By means of NT, we obtain the transformed problem which is then solved by using HPM. By means of Stehfest’s numerical algorithm and using the dual relationship of NT and Laplace transform, we calculate inverse NT for approximate solutions. The series solutions we obtain using the proposed method are in close agreement with the exact solutions. We apply the proposed method to some interesting problems to illustrate our main results.
Shah, Kamal; Khalil, Hammad; and Yildirim, Ahmet
On a Hybrid Technique to Handle Analytical and Approximate Solutions of Linear and Nonlinear Fractional Order Partial Differential Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 14,
2, Article 18.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss2/18