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A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations

A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to... AbstractIn this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional space-time fractional mKDV-ZK equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The Riccati-Bernoulli Sub-ODE method appears to be easier and more convenient by means of a symbolic computation system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations

Abdelrahman, Mahmoud A.E.
Nonlinear Engineering , Volume 7 (4): 7 – Dec 19, 2018
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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
2192-8029
eISSN
2192-8029
DOI
10.1515/nleng-2017-0145
Publisher site
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Abstract

AbstractIn this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Zoomeron equation and the (3 + 1) dimensional space-time fractional mKDV-ZK equation. These nonlinear fractional equations can be turned into another nonlinear ordinary differential equation by complex transform method. This method is efficient and powerful in solving wide classes of nonlinear fractional order equations. The Riccati-Bernoulli Sub-ODE method appears to be easier and more convenient by means of a symbolic computation system.

Journal

Nonlinear Engineering – de Gruyter

Published: Dec 19, 2018

References

  • The modified Kudryashov method for solving some fractional-order nonlinear equations
  • Solitary waves for the nonlinear Schrödinger problem with theprobability distribution function in the stochastic input case
  • A generalized exp-function method for fractional riccati differential equations
  • The first integral method for some time fractional differential equations
  • Linear models of dissipation whose Q is almost frequency independent II
  • Exact solutions of a fractional-type differential–difference equation related to discrete MKdV equation