Numerical solution of fractional bioheat equation by quadratic spline collocation method

The time-fractional heat conduction equation with the Caputo derivative and with heat absorption term proportional to temperature is considered in a sphere in the case of central symmetry. The fundamental solution to the Dirichlet boundary value problem is found, and the solution to the problem under constant boundary value of temperature is studied. The integral transform technique is used. The solutions are obtained in terms of series containing the Mittag-Leffler functions being the generalization of the exponential function. The numerical results are illustrated graphically.

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“…(2) in the case of one Cartesian spatial coordinate (Damor et al 2016;Ferrás et al 2015;Qin and Wu 2016;Vitali et al 2017). Here, we study Eq.…”

Section: Introductionmentioning

confidence: 99%

Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition

Povstenko

Klekot

2018

Comp. Appl. Math.

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“…The equation

can be regarded as the time-fractional generalization of the diffusion, bio-heat, and cable equations as well as time-fractional generalization of the Klein–Gordon equation [ 37 , 38 , 39 , 40 , 41 , 42 , 43 ].…”

Section: Introductionmentioning

confidence: 99%

Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

Povstenko

Kyrylych

2018

Entropy

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The time-fractional diffusion equation with mass absorption is studied in a half-line domain under the Dirichlet boundary condition varying harmonically in time. The Caputo derivative is employed. The solution is obtained using the Laplace transform with respect to time and the sin-Fourier transform with respect to the spatial coordinate. The results of numerical calculations are illustrated graphically.

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“…The temperature distribution in the skin tissue is very important for medical application such as skin cancer, skin burns ,etc [9]. The fractional bioheat model has attracted the focus of the researchers and it contributes to a significant rate of the ongoing research [10][11][12][13][14][15][16][17][18]. In this work, we introduce a numerical approach for solving the one-dimensional S-FBHE based on FSLPs.…”

Section: Al-saadawi and Al-humedimentioning

confidence: 99%

The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials

Al-Saadawi

Al-Humedi

2020

eijs

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The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

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Numerical solution of fractional bioheat equation by quadratic spline collocation method

Cited by 21 publications

References 31 publications

Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition

Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition

Time-Fractional Diffusion with Mass Absorption in a Half-Line Domain due to Boundary Value of Concentration Varying Harmonically in Time

The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials

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