Travelling wave solutions for fractional Boussinesq equation using modified (G’/G) expansion method

Al-Shawba, Altaf A.; Abdullah, Farah Aini; Azmi, Amirah

doi:10.1063/1.5041567

Cited by 8 publications

(7 citation statements)

References 15 publications

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“…Inserting the values of the parameters assembled in (21) into solution (19) along with (6) and (16), the following wide-ranging hyperbolic function solution is ascertained:…”

Section: Complexitymentioning

confidence: 99%

“…Substituting the values scheduled in (29) into solution (19) along with (8) and (16), the succeeding trigonometric solution to the CRWP equation 15is established:…”

Section: Complexitymentioning

confidence: 99%

“…e exact solutions of nonlinear FDEs play fundamental role in describing different qualitative and quantitative features of nonlinear complex physical phenomena. For this reason, researchers have proposed different methods to obtain exact solutions to nonlinear FDEs such as exp(− φ(ξ))-expansion method [9][10][11][12], the (G′/G)-expansion method [13][14][15][16][17][18][19], auxiliary equation method [20,21], (G ′ /G, 1/G)-expansion method [22][23][24][25][26][27] the trial equation method [28,29], fractional subequation method [30,31], modified simple equation method [32], generalized Kudrayshov method [33,34], and others [35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

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An Extension of the Double $(G^{'} / G,)$
Al-Shawba
¹
,
Abdullah
²
,
Azmi
³

et al. 2020
Complexity
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6
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The phenomena, molecular path in a liquid or a gas, fluctuating price stoke, fission and fusion, quantum field theory, relativistic wave motion, etc., are modeled through the nonlinear time fractional clannish random Walker’s parabolic (CRWP) equation, nonlinear time fractional SharmaTassoOlver (STO) equation, and the nonlinear space-time fractional KleinGordon equation. The fractional derivative is described in the sense of conformable derivative. From there, the G ′ / G , 1 / G -expansion method is found to be ensuing, effective, and capable to provide functional solutions to nonlinear models concerning physical and engineering problems. In this study, an extension of the G ′ / G , 1 / G -expansion method has been introduced. This enhancement establishes broad-ranging and adequate fresh solutions. In addition, some existing solutions attainable in the literature also confirm the validity of the suggested extension. We believe that the extension might be added to the literature as a reliable and efficient technique to examine a wide variety of nonlinear fractional systems with parameters including solitary and periodic wave solutions to nonlinear FDEs.

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“…Inserting the values of the parameters assembled in (21) into solution (19) along with (6) and (16), the following wide-ranging hyperbolic function solution is ascertained:…”

Section: Complexitymentioning

confidence: 99%

“…Substituting the values scheduled in (29) into solution (19) along with (8) and (16), the succeeding trigonometric solution to the CRWP equation 15is established:…”

Section: Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Extension of the Double $(G^{'} / G,)$
Al-Shawba
¹
,
Abdullah
²
,
Azmi
³

et al. 2020
Complexity
Self Cite
6
0
0
0
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“…This equation seems within the electric circuit and multi constituent plasms and fluid mechanics, signal processing, hydrology, viscoelasticity and so on. Sohail, et al [40] proposed method known as the G′/G-expansion method and the fractional complex transform are successfully employed to obtain the exact solutions of fractional modified third-order KdV equations. Shah et al [41] applied Adomian decomposition to display the efficiency of the technic used for together fractional and integer order the space of time-fractional modified third-order Kdv equation.…”

Section: Introductionmentioning

confidence: 99%

Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique

Sadia¹,

Arefin²,

Uddin³

2021

Preprint

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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 (NLFDEs) to translate into the ordinary differential equation employing wave alteration. To explore such categories of resolutions, the extended tanh-method is accomplished via Conformable fractional 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. To convert this problem to a standard differential equation, a partial complex transformation that has been summarized succinctly is utilized correctly thus, with all of the free parameters, numerous exact logical arrangements are required. The results are found as hyperbolic and rational functions involving parameters, when specific values are supplied to the parameters solitary wave solutions are formed from traveling wave solutions. 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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“…Several efficient methods have recently been developed to get analytical solutions for FDEs. For example, the generalized tanh-coth method [10], the auxiliary equation method [11], the ( G G )-expansion method [12][13][14][15][16][17][18][19][20][21][22][23], the improved F-expansion method [24], the exponential rational function method [25][26][27], the simplest equation method [28], the modified simple equation method [29][30][31][32], the first integral method [33][34][35][36][37], the Kudryashov method [38][39][40][41][42][43], the modified extended tanh expansion method [44], the ( G G , 1 G )-expansion method [45][46][47][48][49][50][51], etc. [52][53][54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G

et al. 2018

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In this paper, the two variables ( G G , 1 G )-expansion method is applied to obtain new exact solutions with parameters of higher-dimensional nonlinear time-fractional differential equations (NTFDEs) in the sense of the conformable fractional derivative. To clarify the veracity of this method, it is implemented in nonlinear (2 + 1)-dimensional time-fractional biological population (BP) model and nonlinear (3 + 1)-dimensional KdV-Zakharov-Kuznetsov (KdV-ZK) equation with time-fractional derivative. When the parameters take some special values, the solitary and periodic solutions are obtained from the hyperbolic and trigonometric function solutions.

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Travelling wave solutions for fractional Boussinesq equation using modified (G’/G) expansion method

Cited by 8 publications

References 15 publications

An Extension of the Double $(G^{'} / G,)$
Al-Shawba
¹
,
Abdullah
²
,
Azmi
³

et al. 2020
Complexity
Self Cite
6
0
0
0
View full text Add to dashboard Cite

An Extension of the Double $(G^{'} / G,)$
Al-Shawba
¹
,
Abdullah
²
,
Azmi
³

et al. 2020
Complexity
Self Cite
6
0
0
0
View full text Add to dashboard Cite

Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G

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Travelling wave solutions for fractional Boussinesq equation using modified (G’/G) expansion method

Cited by 8 publications

References 15 publications

An Extension of the Double G ′ / G , Al-Shawba1, Abdullah2, Azmi3 et al. 2020ComplexitySelf Cite6000View full textAdd to dashboardCite

An Extension of the Double G ′ / G , Al-Shawba1, Abdullah2, Azmi3 et al. 2020ComplexitySelf Cite6000View full textAdd to dashboardCite

Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G

Contact Info

Product

Resources

About

An Extension of the Double $(G^{'} / G,)$
Al-Shawba
¹
,
Abdullah
²
,
Azmi
³

et al. 2020
Complexity
Self Cite
6
0
0
0
View full text Add to dashboard Cite

An Extension of the Double $(G^{'} / G,)$
Al-Shawba
¹
,
Abdullah
²
,
Azmi
³

et al. 2020
Complexity
Self Cite
6
0
0
0
View full text Add to dashboard Cite