Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas
The present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing the unsteady-flow of polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, two efficient hybrid methods so-called optimal homo...
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/285 |
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| author | Brajesh K. Singh Haci Mehmet Baskonus Neetu Singh Mukesh Gupta D. G. Prakasha |
| author_facet | Brajesh K. Singh Haci Mehmet Baskonus Neetu Singh Mukesh Gupta D. G. Prakasha |
| author_sort | Brajesh K. Singh |
| collection | DOAJ |
| description | The present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing the unsteady-flow of polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, two efficient hybrid methods so-called optimal homotopy analysis <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-transform method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>O</mi></msub></semantics></math></inline-formula>HA<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>TM) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-variational iteration transform method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM) have been adopted. The <sub><i>O</i></sub>HA<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>TM is the hybrid method, where optimal-homotopy analysis method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>O</mi></msub></semantics></math></inline-formula>HAM) is utilized after implementing the properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-transform (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>T), and in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM is the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-transform-based variational iteration method. Banach’s fixed point approach is adopted to analyze the convergence of these methods. It is demonstrated that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">T</mi></semantics></math></inline-formula>-stable, and the evaluated dynamics of pGas are described in terms of Mittag–Leffler functions. The proposed evaluation confirms that the implemented methods perform better for the referred model equation of pGas. In addition, for a given iteration, the proposed behavior via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>O</mi></msub></semantics></math></inline-formula>HA<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>TM performs better in producing more accurate behavior in comparison to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM and the methods introduced recently. |
| first_indexed | 2024-03-11T06:56:23Z |
| format | Article |
| id | doaj.art-5221d080482c465689bed87a78dc227c |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:56:23Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5221d080482c465689bed87a78dc227c2023-11-17T09:35:22ZengMDPI AGAxioms2075-16802023-03-0112328510.3390/axioms12030285Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic GasBrajesh K. Singh0Haci Mehmet Baskonus1Neetu Singh2Mukesh Gupta3D. G. Prakasha4School of Physical and Decision Sciences, Department of Mathematics, Babasaheb Bhimrao Ambedkar University Lucknow, Lucknow 226025, IndiaDepartment of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa 63100, TurkeySchool of Physical and Decision Sciences, Department of Mathematics, Babasaheb Bhimrao Ambedkar University Lucknow, Lucknow 226025, IndiaSchool of Physical and Decision Sciences, Department of Mathematics, Babasaheb Bhimrao Ambedkar University Lucknow, Lucknow 226025, IndiaDepartment of Mathematics, Davangere University, Davangere 577007, IndiaThe present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing the unsteady-flow of polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, two efficient hybrid methods so-called optimal homotopy analysis <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-transform method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>O</mi></msub></semantics></math></inline-formula>HA<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>TM) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-variational iteration transform method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM) have been adopted. The <sub><i>O</i></sub>HA<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>TM is the hybrid method, where optimal-homotopy analysis method (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>O</mi></msub></semantics></math></inline-formula>HAM) is utilized after implementing the properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-transform (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>T), and in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM is the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-transform-based variational iteration method. Banach’s fixed point approach is adopted to analyze the convergence of these methods. It is demonstrated that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">T</mi></semantics></math></inline-formula>-stable, and the evaluated dynamics of pGas are described in terms of Mittag–Leffler functions. The proposed evaluation confirms that the implemented methods perform better for the referred model equation of pGas. In addition, for a given iteration, the proposed behavior via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>O</mi></msub></semantics></math></inline-formula>HA<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>TM performs better in producing more accurate behavior in comparison to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">J</mi></semantics></math></inline-formula>-VITM and the methods introduced recently.https://www.mdpi.com/2075-1680/12/3/285caputo derivativepolytropic gas?-transformvariational calculusoptimal homotopy analysis method |
| spellingShingle | Brajesh K. Singh Haci Mehmet Baskonus Neetu Singh Mukesh Gupta D. G. Prakasha Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas Axioms caputo derivative polytropic gas ?-transform variational calculus optimal homotopy analysis method |
| title | Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas |
| title_full | Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas |
| title_fullStr | Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas |
| title_full_unstemmed | Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas |
| title_short | Study of Time-Fractional Nonlinear Model Governing Unsteady Flow of Polytropic Gas |
| title_sort | study of time fractional nonlinear model governing unsteady flow of polytropic gas |
| topic | caputo derivative polytropic gas ?-transform variational calculus optimal homotopy analysis method |
| url | https://www.mdpi.com/2075-1680/12/3/285 |
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