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E M Abulwafa - One of the best experts on this subject based on the ideXlab platform.

  • formulation and solution of space time fractional Boussinesq Equation
    Nonlinear Dynamics, 2015
    Co-Authors: S A Elwakil, E M Abulwafa
    Abstract:

    The fractional variational principles beside the semi-inverse technique are applied to derive the space–time fractional Boussinesq Equation. The semi-inverse method is used to find the Lagrangian of the Boussinesq Equation. The classical derivatives in the Lagrangian are replaced by the fractional derivatives. Then, the fractional variational principles are devoted to lead to the fractional Euler–Lagrange Equation, which gives the fractional Boussinesq Equation. The modified Riemann–Liouville fractional derivative is used to obtain the space–time fractional Boussinesq Equation. The fractional sub-Equation method is employed to solve the derived space-time fractional Boussinesq Equation. The solutions are obtained in terms of fractional hyper-geometric functions, fractional triangle functions and a rational function. These solutions show that the fractional Boussinesq Equation can describe periodic, soliton and explosive waves. This study indicates that the fractional order modulates the waves described by Boussinesq Equation. We remark that more pronounced effects and deeper insight into the formation and properties of the resulting waves are added by considering the fractional order derivatives beside the nonlinearity.

  • Formulation and solution of space–time fractional Boussinesq Equation
    Nonlinear Dynamics, 2015
    Co-Authors: S.a. El-wakil, E M Abulwafa
    Abstract:

    The fractional variational principles beside the semi-inverse technique are applied to derive the space–time fractional Boussinesq Equation. The semi-inverse method is used to find the Lagrangian of the Boussinesq Equation. The classical derivatives in the Lagrangian are replaced by the fractional derivatives. Then, the fractional variational principles are devoted to lead to the fractional Euler–Lagrange Equation, which gives the fractional Boussinesq Equation. The modified Riemann–Liouville fractional derivative is used to obtain the space–time fractional Boussinesq Equation. The fractional sub-Equation method is employed to solve the derived space-time fractional Boussinesq Equation. The solutions are obtained in terms of fractional hyper-geometric functions, fractional triangle functions and a rational function. These solutions show that the fractional Boussinesq Equation can describe periodic, soliton and explosive waves. This study indicates that the fractional order modulates the waves described by Boussinesq Equation. We remark that more pronounced effects and deeper insight into the formation and properties of the resulting waves are added by considering the fractional order derivatives beside the nonlinearity.

Hossein Jafari - One of the best experts on this subject based on the ideXlab platform.

  • fractional lie group method of the time fractional Boussinesq Equation
    Nonlinear Dynamics, 2015
    Co-Authors: Hossein Jafari, Nematollah Kadkhoda, Dumitru Baleanu
    Abstract:

    Finding the symmetries of the nonlinear fractional differential Equations is a topic which has many applications in various fields of science and engineering. In this manuscript, firstly, we are interested in finding the Lie point symmetries of the time-fractional Boussinesq Equation. After that, by using the infinitesimal generators, we determine their corresponding invariant solutions.

  • Derivation of a fractional Boussinesq Equation for modelling unconfined groundwater
    European Physical Journal-special Topics, 2013
    Co-Authors: Behrouz Mehdinejadiani, Hossein Jafari, Dumitru Baleanu
    Abstract:

    In this manuscript, a fractional Boussinesq Equation is obtained by assuming power-law changes of flux in a control volume and using a fractional Taylor series. Furthermore, it was assumed that the average thickness of the watery layer of an aquifer is constant, and the linear fractional Boussinesq Equation was derived. Unlike classical Boussinesq Equation, due to the non-locality property of fractional derivatives, the parameters of the fractional Boussinesq Equation are constant and scale-invariant. In addition, the fractional Boussinesq Equation has two various fractional orders of differentiation with respect to x and y that indicate the degree of heterogeneity in the x and y directions, respectively.

Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.

  • fractional lie group method of the time fractional Boussinesq Equation
    Nonlinear Dynamics, 2015
    Co-Authors: Hossein Jafari, Nematollah Kadkhoda, Dumitru Baleanu
    Abstract:

    Finding the symmetries of the nonlinear fractional differential Equations is a topic which has many applications in various fields of science and engineering. In this manuscript, firstly, we are interested in finding the Lie point symmetries of the time-fractional Boussinesq Equation. After that, by using the infinitesimal generators, we determine their corresponding invariant solutions.

  • Derivation of a fractional Boussinesq Equation for modelling unconfined groundwater
    European Physical Journal-special Topics, 2013
    Co-Authors: Behrouz Mehdinejadiani, Hossein Jafari, Dumitru Baleanu
    Abstract:

    In this manuscript, a fractional Boussinesq Equation is obtained by assuming power-law changes of flux in a control volume and using a fractional Taylor series. Furthermore, it was assumed that the average thickness of the watery layer of an aquifer is constant, and the linear fractional Boussinesq Equation was derived. Unlike classical Boussinesq Equation, due to the non-locality property of fractional derivatives, the parameters of the fractional Boussinesq Equation are constant and scale-invariant. In addition, the fractional Boussinesq Equation has two various fractional orders of differentiation with respect to x and y that indicate the degree of heterogeneity in the x and y directions, respectively.

S A Elwakil - One of the best experts on this subject based on the ideXlab platform.

  • formulation and solution of space time fractional Boussinesq Equation
    Nonlinear Dynamics, 2015
    Co-Authors: S A Elwakil, E M Abulwafa
    Abstract:

    The fractional variational principles beside the semi-inverse technique are applied to derive the space–time fractional Boussinesq Equation. The semi-inverse method is used to find the Lagrangian of the Boussinesq Equation. The classical derivatives in the Lagrangian are replaced by the fractional derivatives. Then, the fractional variational principles are devoted to lead to the fractional Euler–Lagrange Equation, which gives the fractional Boussinesq Equation. The modified Riemann–Liouville fractional derivative is used to obtain the space–time fractional Boussinesq Equation. The fractional sub-Equation method is employed to solve the derived space-time fractional Boussinesq Equation. The solutions are obtained in terms of fractional hyper-geometric functions, fractional triangle functions and a rational function. These solutions show that the fractional Boussinesq Equation can describe periodic, soliton and explosive waves. This study indicates that the fractional order modulates the waves described by Boussinesq Equation. We remark that more pronounced effects and deeper insight into the formation and properties of the resulting waves are added by considering the fractional order derivatives beside the nonlinearity.

Anjan Biswas - One of the best experts on this subject based on the ideXlab platform.