Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

By Ahmet Bekir, Ozkan Guner, Adem C. Cevikel. 2013

142 citations recorded by the source corpus.

The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/79ff99a043e6b5e6d194ae43ec4fe9762881b5e2

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In Modeling and Simulation

1. Esin Aksoy
2. Ahmet Bekir
3. Adem C. Cevikel
4. N. Kudryashov

In Numerical Analysis

1. Esin Aksoy
2. Ahmet Bekir
3. Adem C. Cevikel

In Statistical and Nonlinear Physics

1. Esin Aksoy
2. Ahmet Bekir
3. Adem C. Cevikel
4. N. Kudryashov

Citations in the corpus

• Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method (2015, methodology): “In recent years, many powerful and efficient methods have been proposed to obtain exact solutions of partial differential equations, such as the fractional sub-equation method [6–9], the (G’/G)-expansion method [10, 11], the exp-function method [12, 13], the first integral method [14], the functiona”