The Extended Trial Equation Method for Some Time Fractional Differential Equations
By Y. Pandır, Yusuf Gurefe, E. Mısırlı. 2013
73 citations recorded by the source corpus.
Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractional equation according to the complete discrimination system for polynomial method. As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions.
Subfields: Geometry and Topology, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/52e130b5cad8e6c11143184653db1b6e0a4797b6
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Citations in the corpus
- Counterexamples on Jumarie's three basic fractional calculus formulae for non-differentiable continuous functions (2016, methodology): “The formula (3) has been applied to solve the exact solutions to some nonlinear fractional order differential equations(see, for example, Refs.”
- All exact travelling wave solutions of Hirota equation and Hirota–Maccari system (2016, methodology): “In this work, the extended trial equation method [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24] and generalized Kudryashov method [6, 7] will be applied to obtain exact solutions of Hirota equation and Hirota-Maccari system.”