Numerical Solution of Space-Time Fractional Klein-Gordon Equation by Radial Basis Functions and Chebyshev Polynomials

Bansu, Hitesh; Kumar, Sushil

doi:10.1007/s40819-021-01139-7

Cited by 9 publications

(3 citation statements)

References 29 publications

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“…Khan et al (2019) developed a numerical technique with the advantage of the Sumudu decomposition method to solve the Caputo fractional K-G equation. Singh et al (2020) presented a computational technique by combining of collocation method with orthogonal polynomial matrices while Bansu and Kumar (2021) presented a novel collocation method to solve the space-time fractional K-G equation. Khader and Adel (2016) used variational iteration methods with fractional complex transform to solve the fractional K-G equation.…”

Section: Introductionmentioning

confidence: 99%

Approximation of the Time-Fractional Klein-Gordon Equation using the Integral and Projected Differential Transform Methods

Singh

2023

Int. j. math. eng. manag. sci.

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In the present investigation, a new integral transform method (NITM) and the projected differential transform method (PDTM) are used to give an analytical solution to the time-fractional Klein-Gordon (TFKG) equation. The time-fractional derivative is used in the Caputo sense. The huge advantage of the suggested approach is the ease with which the nonlinear term can be effortlessly treated by projected differential transform without using Adomian's and He's polynomials. The solution of fractional partial differential equations using the aforementioned method is very simple and straightforward. The efficiency and accuracy of the proposed method are demonstrated by three examples, and the effects of various fractional Brownian motions are demonstrated graphically.

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Section: Introductionmentioning

confidence: 99%

Approximation of the Time-Fractional Klein-Gordon Equation using the Integral and Projected Differential Transform Methods

Singh

2023

Int. j. math. eng. manag. sci.

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“…Tamsir and Srivastava [16] used fractional reduced differential transform to obtain the analytical solution of linear and nonlinear KG equation with time-fractional order. Bansu and Kumar [17] used a radial basis approach, and Kurulay [18] applied the homotopy analysis method to evaluate the numerical solution of the space-time fractional KG equation. Later, Khader and Adel [19] applied a hybridization scheme to achieve the solution of the fractional KG equation.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solution of Nonlinear Time-Fractional Klein-Gordon Equations Using Yang Transform

et al. 2022

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The algebras of the symmetry operators for the Klein–Gordon equation are important for a charged test particle, moving in an external electromagnetic field in a space time manifold on the isotropic hydrosulphate. In this paper, we develop an analytical and numerical approach for providing the solution to a class of linear and nonlinear fractional Klein–Gordon equations arising in classical relativistic and quantum mechanics. We study the Yang homotopy perturbation transform method (YHPTM), which is associated with the Yang transform (YT) and the homotopy perturbation method (HPM), where the fractional derivative is taken in a Caputo–Fabrizio (CF) sense. This technique provides the solution very accurately and efficiently in the form of a series with easily computable coefficients. The behavior of the approximate series solution for different fractional-order ℘ values has been shown graphically. Our numerical investigations indicate that YHPTM is a simple and powerful mathematical tool to deal with the complexity of such problems.

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“…Kheiri et al [12] studied a non-homogeneous fractional Klein-Gordon equation with Dirichlet, Neumann, and Robin boundary conditions using the separating variables method. Other studies regarding the Klein-Gordon equation can be found in the references [3,13,8,14].…”

Section: Introductionmentioning

confidence: 99%

"General analytical solution of fractional Klein–Gordon equation in a spherical domain"

FETECAU¹,

VIERU²

2022

CJM

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"Time-fractional Klein–Gordon equation in a sphere is considered for the case of central sym- metry under the time-variable Dirichlet condition. The time-fractional derivative with the power-law kernel is used. The Laplace transform and convenient transformations of the independent variable and unknown func- tion are used to determine the general analytical solution of the problem in the Laplace domain. In order to obtain the solution in the real domain, the inverse Laplace transforms of two functions of exponential type whose expressions are new in the literature have been determined. The similar solution for ordinary Klein– Gordon equation is a limiting case of general solution but a simpler form for this solution is provided. The convergence of general solution to the ordinary solution and the effects of fractional parameter on this solution are graphically underlined."

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Numerical Solution of Space-Time Fractional Klein-Gordon Equation by Radial Basis Functions and Chebyshev Polynomials

Cited by 9 publications

References 29 publications

Approximation of the Time-Fractional Klein-Gordon Equation using the Integral and Projected Differential Transform Methods

Approximation of the Time-Fractional Klein-Gordon Equation using the Integral and Projected Differential Transform Methods

Approximate Solution of Nonlinear Time-Fractional Klein-Gordon Equations Using Yang Transform

"General analytical solution of fractional Klein–Gordon equation in a spherical domain"

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