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Adequate soliton solutions to the space–time fractional telegraph equation and modified third-order KdV equation through a reliable technique


The space–time fractional Telegraph equation and the space–time fractional modified third-order Kdv equations are significant molding equations in theoretic physics, mathematical physics, plasma physics also other fields of nonlinear sciences. The space time-fractional telegraph equation, which appears in the investigation of an electrical communication line and includes voltage in addition to current which is dependent on distance and time, is also applied to communication lines of wholly frequencies, together with direct current, as well as high-frequency conductors, audio frequency (such as telephone lines), and low frequency (for example cable television) used in the extension of pressure waves into the lessons of pulsatory blood movement among arteries also the one-dimensional haphazard movement of bugs towards an obstacle. The presence of chain rule and the derivative of composite functions allows the nonlinear fractional differential equations to translate into the ordinary differential equation employing wave alteration. To explore such categories of resolutions, the extended tanh-method is accomplished via Conformable derivatives. A power sequence in tanh was originally used as an ansatz to provide analytical solutions of the traveling wave type of certain nonlinear evolution equations. The outcomes achieved in this study are king type, single soliton, double soliton, multiple solitons, bell shape, and other sorts of forms and we demonstrated that these solutions were validated through the Maple software. The proposed approach for solving nonlinear fractional partial differential equations has been developed to be operative, unpretentious, quick, and reliable to usage.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.


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The authors would like to thank the anonymous referees for their insightful remarks and ideas to improve the article’s quality.


Authors would like to thank the ICT Division of  Bangladesh for supporting the research.

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MAA: Software, Data Curation, Writing, Investigation. US: Software, Data Curation, Writing, Formal Analysis. MI: Investigation, Validation. MHU: Conceptualization, Supervision, Writing-Reviewing Editing, Validation.

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Correspondence to M. Hafiz Uddin.

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Arefin, M.A., Sadiya, U., Inc, M. et al. Adequate soliton solutions to the space–time fractional telegraph equation and modified third-order KdV equation through a reliable technique. Opt Quant Electron 54, 309 (2022).

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