On invariant analysis and conservation laws of the time fractional variant Boussinesq and coupled Boussinesq-Burger’s equations

Hashemi, Mir Sajjad; Balmeh, Z.

doi:10.1140/epjp/i2018-12289-1

Cited by 19 publications

(4 citation statements)

References 31 publications

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“…In this section, we prove that Equation ( 1) is nonlinearly self-contained, and therefore, protection laws can be created for them using their symmetry. In this section, we will discuss the conservation laws 44 for the vector fields obtained from the classical and non-classical types of the Lie symmetry group. First, we give an overview of this method.…”

Section: Conservation Lawmentioning

confidence: 99%

Non‐classical Lie symmetries for nonlinear time‐fractional Heisenberg equations

Hashemi

Haji‐Badali

Alizadeh

et al. 2022

Math Methods in App Sciences

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The current work is based on performing the non‐classical and classical Lie group analysis for a system of nonlinear time‐fractional Heisenberg equation. Here, we apply analysis of the Lie group symmetry as one of the powerful tools dealing with the large class of fractional order differential equations in the Riemann–Liouville (RL) sense. Indeed, classical and non‐classical Lie symmetries group is used to similarity reduction of nonlinear time‐fractional Heisenberg equation. Especially, based on the obtained Lie symmetry generators, we construct conservation laws for the classical and non‐classical vector fields related to the Heisenberg time‐fraction equation.

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Section: Conservation Lawmentioning

confidence: 99%

Non‐classical Lie symmetries for nonlinear time‐fractional Heisenberg equations

Hashemi

Haji‐Badali

Alizadeh

et al. 2022

Math Methods in App Sciences

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show abstract

“…Furthermore, almost studies on the logical and numerical blend (solution) of generalized nonlinear model Eq. ( 1 ) with gas bubbles have been explored in the literature, for example, the bilinear formalism and soliton solutions using Hirota bilinear method 21 , Assemble mixed rogue wave-stripe solitons and mixed lump-stripe solitons 23 , the binary Bell polynomials obtaining the bilinear form of this model 25 , and the solitons and lumps solution for the generalized nonlinear wave 26 . There are numerous fractional derivative operators in fractional calculus, such as the Caputo derivative, Grunwald derivative, Riemann–Liouville derivative, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…( 1 ) via five mathematical methods 50 – 54 , these methods are called ESE method 50 , modified extended AEM approach 51 , -expansion scheme 52 , -expansion method 53 and modified F-expansion method 54 respectively. The investigated our solutions are in different types like exponential, trigonometric, hyperbolic and rational forms and are totally d new solutions as compared to exist in previous literature by using the different techniques of distinct authors on this model 21 , 23 , 25 , 26 .…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the (3+1)-generalized fractional nonlinear wave equation with gas bubbles

Seadawy,

Ali,

Altalbe

et al. 2024

Sci Rep

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In this manuscript, we implement the travelling wave solutions of the fractional (3+1) generalized computational nonlinear wave equation with gas bubbles via application of five mathematical methods. Liquids with gas bubbles primarily arise in various applications like science, engineering, and mathematical physics. The obtained solitary waves solutions have fruitful applications in engineering, science, life, nature and physics. Several novel soliton solutions of concerned model are established in the form of hyperbolic, trigonometric, exponential and rational functions. To handle all calculations and verification of obtained results, computational software Mathematica 12.1 is used. For the demonstration of the physical behaviour of concern model, some solutions are plotted graphical in 2-dimensional and 3-dimensional by imparting specific values to the parameters under constrain conditions. Finally, we intrigue both two and three dimensional to explain the physical behavior of the model.

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“…The approximate and exact solutions are the two categories of solutions that are most frequently explored in research. There are just a few methods, like the Lie symmetry method [7][8][9], and invariant subspace method [10][11][12], for solving differential equations using FDs precisely. Additionally, a variety of approximation techniques are suggested to take into account the numerical solutions of fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Innovative Method for Computing Approximate Solutions of Non-Homogeneous Wave Equations with Generalized Fractional Derivatives

Hashemi,

Mirzazadeh,

Baleanu

2023

Contemp. Math.

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In this work, a well-known non-homogeneous wave equation with temporal fractional derivative is approximately investigated. A recently defined generalized non-local fractional derivative is utilized as the fractional operator. A novel technique is proposed to approximate the solutions of wave equation with generalized fractional derivative. The proposed method is based on the shifted Chebyshev polynomials and a combination of collocation and residual function methods. Theoretical analysis of the convergence of the proposed method is performed. Approximate solutions are derived in both rectangular and non-rectangular (general) domains.

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On invariant analysis and conservation laws of the time fractional variant Boussinesq and coupled Boussinesq-Burger’s equations

Cited by 19 publications

References 31 publications

Non‐classical Lie symmetries for nonlinear time‐fractional Heisenberg equations

Non‐classical Lie symmetries for nonlinear time‐fractional Heisenberg equations

Exact solutions of the (3+1)-generalized fractional nonlinear wave equation with gas bubbles

Innovative Method for Computing Approximate Solutions of Non-Homogeneous Wave Equations with Generalized Fractional Derivatives

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