A new analytical approach to solve some of the fractional-order partial differential equations

作者：Manafian J; Lakestani M

来源：Indian Journal of Physics and Proceedings of the Indian Association for the Cultivation of Science, 2017, 91(3): 243-258.

DOI：10.1007/s12648-016-0912-z

• Generalized tanh-coth method
• Fractional biological population model
• Fractional Burgers
• Fractional Cahn-Hilliard
• Fractional Whitham-Broer-Kaup
• Fractional Fokas

The aim of the present paper is to present an analytical method for the time fractional biological population model, time fractional Burgers, time fractional Cahn-Hilliard, space-time fractional Whitham-Broer-Kaup, space-time fractional Fokas equations by using the generalized tanh-coth method. The fractional derivative is described in the sense of the modified Riemann-Liouville derivatives. The method gives an analytic solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. We have obtained the exact solutions for the aforementioned nonlinear fractional equations. A generalized fractional complex transform is appropriately used to convert these fractional equations to ordinary differential equations which subsequently resulted into number of exact solutions.

• 出版日期2017-3