An efficient hybrid numerical approach for solving two-dimensional fractional cable model involving time-fractional operator of distributed order with error analysis

Kosari, Saeed; Xu, Peng; Shafi, Jana; Derakhshan, MohammadHossein

doi:10.1007/s11075-024-01913-w

Numer Algor

2024

DOI: 10.1007/s11075-024-01913-w

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An efficient hybrid numerical approach for solving two-dimensional fractional cable model involving time-fractional operator of distributed order with error analysis

Saeed Kosari,

Peng Xu,

Jana Shafi

et al.

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2024

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Cited by 2 publications

References 29 publications

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Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Cai,

Kosari,

Shafi

et al. 2024

Phys. Scr.

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In this manuscript, a new model of the time-fractional Galilei-invariant advection-diffusion model of distributed order is studied. An efficient hybrid numerical approach with high accuracy is used to estimate this equation. The finite difference numerical method is used to approximate the fractional operator in terms of the time variable and to approximate the integral term of distributed order, the Gaussian--Legendre integration is applied. To obtain a fully discrete numerical approach, we used a spectral element numerical approach, in which Legendre polynomials are used as the basis function. For the proposed numerical approach, the error and stability analysis are studied. For the efficiency of the numerical approach, some numerical examples are presented with graphs and tables.

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Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Cai,

Kosari,

Shafi

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform

Chen,

Kosari,

Shafi

et al. 2024

Fractal Fract

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In this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the frame of the Caputo–Prabhakar (CP) operator. The nonlinear terms are handled with the assistance of the homotopy polynomials. The stability analysis of the implemented method is studied by using S-stable mapping and the Banach contraction principle. Also, we use the fixed-point method to determine the existence and uniqueness of solutions in the given suggested model. Finally, some numerical simulations are illustrated to display the accuracy and efficiency of the present numerical method. Moreover, numerical behaviors are captured to validate the reliability and efficiency of the scheme.

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An efficient hybrid numerical approach for solving two-dimensional fractional cable model involving time-fractional operator of distributed order with error analysis

Cited by 2 publications

References 29 publications

Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Stability analysis study for the time-fractional Galilei invariant advection-diffusion model of distributive order using an efficient hybrid approach

Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform

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