Analytic solutions for a modified fractional three wave interaction equations with conformable derivative by unified method
| Autor: | Mohammed Al-Smadi, Shaher Momani, Adeeb G. Talafha, Sahar M. Alqaraleh, Samir Hadid |
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| Rok vydání: | 2020 |
| Předmět: |
Infinite set
Work (thermodynamics) 020209 energy Operator (physics) Rational solution Mathematical analysis General Engineering Order (ring theory) Three wave interaction equations Conformable fractional derivative 02 engineering and technology Derivative Conformable matrix Engineering (General). Civil engineering (General) 01 natural sciences 010305 fluids & plasmas Fractional calculus 0103 physical sciences Lax-pair 0202 electrical engineering electronic engineering information engineering Unified method Partial derivative TA1-2040 Mathematics |
| Zdroj: | Alexandria Engineering Journal, Vol 59, Iss 5, Pp 3731-3739 (2020) |
| ISSN: | 1110-0168 |
| Popis: | The present work implements the unified method to a class of fractional partial differential systems corresponding to modified fractional three wave interaction equations (FTWIEs). The fractional derivative of the three waves envelopes is considered under the conformable sense. The conformable FTWIEs is derived in the (3 + 1) dimensions under the conformable time-fractional derivative of order α ∈ ( 0 , 1 ] based on a modification of the Lax-pair created by Zakharov-Manakov which includes three-dimensional velocity vector dotted with the usual del operator. Then, the unified method for creating solutions for nonlinear evolution FTWIEs is applied. Subsequently, a systematic algorithm is used to obtain an infinite set of exact rational solutions to the novel constructed system. By randomly selecting the special values for the parameters, three-dimensional graphs are also given for different patterns. The obtained solutions might play an essential role in many other nonlinear evolution equations that occur in the fields of engineering and mathematical physics. |
| Databáze: | OpenAIRE |
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