A comprehensive numerical study of space-time fractional bioheat equation using fractional-order Legendre functions

Roohi, Reza; Heydari, Mohammad Hossein; Aslami, Mojtaba; Mahmoudi, Mohammad Reza

doi:10.1140/epjp/i2018-12204-x

Cited by 43 publications

(16 citation statements)

References 29 publications

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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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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 problem of the time fractional Pennes bioheat transfer equation for the modeling of skin tissue heat transfer is expressed in previous works [6,14,15,16] [2][3][4][5][6], [8][9][10][11][12][13][14], [16], [17][18][19][20][21] as: ∫…”

Section: Pennes Bioheat Transfer Equation With Time Fractional Derivamentioning

confidence: 99%

“…Definition 2: The Caputo fractional derivative of order is defined by [2][3][4][5][6], [8][9][10][11][12][13][14], [16], [19][20][21] as: ∫…”

Section: Pennes Bioheat Transfer Equation With Time Fractional Derivamentioning

confidence: 99%

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A New Mixed Nonpolynomial Spline Method for the Numerical Solutions of Time Fractional Bioheat Equation

Abdullhussein

Al-Humedi

2020

eijs

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In this paper, a numerical approximation for a time fractional one-dimensional bioheat equation (transfer paradigm) of temperature distribution in tissues is introduced. It deals with the Caputo fractional derivative with order for time fractional derivative and new mixed nonpolynomial spline for second order of space derivative. We also analyzed the convergence and stability by employing Von Neumann method for the present scheme.

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“…Gupta et al (2010) proposed a mathematical model for describing the process of heat transfer in biological tissues for different coordinate system during thermal therapy. Roohi et al (2018) found the general form of the space-time-fractional heat conduction equation with locally variable initial condition and time-dependent boundary conditions. Ganesan and Lingeshwaran (2017) proposed a finite-element scheme using the Galerkin finite-element method for computations of the cancer invasion model.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

et al. 2020

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This paper addresses the application of generalized polynomials for solving nonlinear systems of fractional-order partial differential equations with initial conditions. First, the solutions are expanded by means of generalized polynomials through an operational matrix. The unknown free coefficients and control parameters of the expansion with generalized polynomials are evaluated by means of an optimization process relating the nonlinear systems of fractionalorder partial differential equations with the initial conditions. Then, the Lagrange multipliers are adopted for converting the problem into a system of algebraic equations. The convergence of the proposed method is analyzed. Several prototype problems show the applicability of the algorithm. The approximations obtained by other techniques are also tested confirming the high accuracy and computational efficiency of the proposed approach.

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A comprehensive numerical study of space-time fractional bioheat equation using fractional-order Legendre functions

Cited by 43 publications

References 29 publications

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

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

A New Mixed Nonpolynomial Spline Method for the Numerical Solutions of Time Fractional Bioheat Equation

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

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