Some new solutions of the Caudrey–Dodd–Gibbon (CDG) equation using the conformable derivative View Full Text


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Article Info

DATE

2019-03-05

AUTHORS

Sadaf Bibi, Naveed Ahmed, Imran Faisal, Syed Tauseef Mohyud-Din, Muhammad Rafiq, Umar Khan

ABSTRACT

New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to figure out twenty-seven forms of exact solutions, which are soliton, rational, and periodic ones. Also, for some suitable values of parameters, the exact solutions are found, namely dark, bell type, periodic, soliton, singular soliton, and several others, by using the conformable derivative. These types of solutions have not been proclaimed so far. 2D and 3D graphical patterns of some solutions are also given for clarification of physical features. The conformable derivative is one of the excellent choices to solve the nonlinear conformable problems arising in theory of solitons and many other areas. The results are new and very interesting for the large community of researchers working in the field of mathematics and mathematical physics. More... »

PAGES

89

References to SciGraph publications

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  • 2018-03-09. The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel in ADVANCES IN DIFFERENCE EQUATIONS
  • 2015-12-21. Exact travelling wave Solutions for some nonlinear time fractional fifth-order Caudrey–Dodd–Gibbon equation by G′/G-expansion method in SEMA JOURNAL
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  • 2018-07-03. New aspects of poor nutrition in the life cycle within the fractional calculus in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2018-05-26. On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel in NONLINEAR DYNAMICS
  • 2017-01-23. Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative in THE EUROPEAN PHYSICAL JOURNAL PLUS
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  • 2018-02-22. A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel in THE EUROPEAN PHYSICAL JOURNAL PLUS
  • 2015-10-27. The first integral method for Wu–Zhang system with conformable time-fractional derivative in CALCOLO
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    http://scigraph.springernature.com/pub.10.1186/s13662-019-2030-7

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