A Numerical Approach of a Time Fractional Reaction–Diffusion Model with a Non-Singular Kernel

Abbas, Muhammad; Ali, Ajmal; Iqbal, Azhar; Băleanu, Dumitru

doi:10.3390/sym12101653

Cited by 30 publications

(13 citation statements)

References 39 publications

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“…20 Yuan 21 used the Fourier-like spectral approach to solve fractional reaction-diffusion equations in unbounded domains. Akram et al 22 developed an implicit numerical technique for the TFRDEs that is based on extended cubic B-spline and Caputo-Fabrizio fractional derivative methodologies. In Jiang et al, 4 the pure mesh-free method based on the finite-difference scheme has been developed to solve the variable-order time-fractional convection-diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations

Hadhoud

Rageh

Agarwal³

2022

Math Methods in App Sciences

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This paper proposes the shifted Legendre Gauss–Lobatto collocation (SL‐GLC) scheme to solve two‐dimensional space‐fractional coupled reaction–diffusion equations (SFCRDEs). The proposed method is implemented by expressing the function and its spatial fractional derivatives as a finite expansion of shifted Legendre polynomials. Then the expansion coefficients are determined by reducing the SFCRDEs with their initial and boundary conditions to a system of ordinary differential equations for these coefficients. Subsequently, we applied the proposed method to discretize the temporal and spatial variables to convert the two‐dimensional spacetime fractional coupled reaction–diffusion equations (STFCRDEs) to a system of algebraic equations. Some results regarding the error estimation are obtained. Several examples are discussed to validate the capability and efficiency of the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations

Hadhoud

Rageh

Agarwal³

2022

Math Methods in App Sciences

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“…Therefore, numerical solutions are actively being found by proposing new numerical approximation techniques to solve the FDEs. Some notable numerical methods have been developed to solve the fractional partial derivatives problems [1,2,14,19,20,29].…”

Section: Introductionmentioning

confidence: 99%

Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR

et al. 2021

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This paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing the second-order quarter-sweep finite-difference scheme and the preconditioned accelerated over-relaxation method. The proposed numerical method offers an efficient solution to the time-fractional differential equation by applying the computational complexity reduction approach by the quarter-sweep technique. The finite-difference approximation equation will be formulated based on the Caputo’s time-fractional derivative and quarter-sweep central difference in space. The developed approximation equation generates a linear system on a large scale and has sparse coefficients. With the quarter-sweep technique and the preconditioned iterative method, computing the time-fractional differential equation solutions can be more efficient in terms of the number of iterations and computation time. The quarter-sweep computes a quarter of the total mesh points using the preconditioned iterative method while maintaining the solutions’ accuracy. A numerical example will demonstrate the efficiency of the proposed quarter-sweep preconditioned accelerated over-relaxation method against the half-sweep preconditioned accelerated over-relaxation, and the full-sweep preconditioned accelerated over-relaxation methods. The numerical finding showed that the quarter-sweep finite difference scheme and preconditioned accelerated over-relaxation method can serve as an efficient numerical method to solve fractional differential equations.

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“…The B-spline was proposed by many authors to solve fractional partial differential models [31][32][33][34][35][36][37][38]. These functions can adjust every point in the domain and approximate the solution with maximum frequency accuracy.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

2021

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Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

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A Numerical Approach of a Time Fractional Reaction–Diffusion Model with a Non-Singular Kernel

Cited by 30 publications

References 39 publications

Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations

Numerical method for solving two‐dimensional of the space and space–time fractional coupled reaction‐diffusion equations

Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR

A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

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