An efficient modified hybrid explicit group iterative method for the time-fractional diffusion equation in two space dimensions

Salama, Fouad Mohammad; Hamid, Nur Nadiah Abd; Ali, Norhashidah Hj. Mohd.; Ali, Umair

doi:10.3934/math.2022134

Cited by 17 publications

(7 citation statements)

References 42 publications

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“…The integer order shows remembrance, whereas, the memory function represents the form of FO. The FO form is applied to the application of the real-world systems [26][27][28][29][30][31][32][33][34]. Few novel features of the ANNs-LMBM for the FO-NEE model are provided as:…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Weera¹,

Zamart²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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The motive of these investigations is to provide the importance and significance of the fractional order (FO) derivatives in the nonlinear environmental and economic (NEE) model, i.e., FO-NEE model. The dynamics of the NEE model achieves more precise by using the form of the FO derivative. The investigations through the non-integer and nonlinear mathematical form to define the FO-NEE model are also provided in this study. The composition of the FO-NEE model is classified into three classes, execution cost of control, system competence of industrial elements and a new diagnostics technical exclusion cost. The mathematical FO-NEE system is numerically studied by using the artificial neural networks (ANNs) along with the Levenberg-Marquardt backpropagation method (ANNs-LMBM). Three different cases using the FO derivative have been examined to present the numerical performances of the FO-NEE model. The data is selected to solve the mathematical FO-NEE system is executed as 70% for training and 15% for both testing and certification. The exactness of the proposed ANNs-LMBM is observed through the comparison of the obtained and the Adams-Bashforth-Moulton database results. To ratify the aptitude, validity, constancy, exactness, and competence of the ANNs-LMBM, the numerical replications using the state transitions, regression, correlation, error histograms and mean square error are also described.

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Section: Introductionmentioning

confidence: 99%

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Weera¹,

Zamart²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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“…They have been used for efficient computations of accurate numerical solutions to the two-dimensional fractional diffusion equation (Salama et al. 2022a ), two-dimensional fractional cable equation (Salama and Abd Hamid 2020 ; Khan et al. 2021 ), two-dimensional fractional reaction diffusion equation (Abdi et al.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

et al. 2023

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The time-fractional advection–diffusion reaction equation (TFADRE) is a fundamental mathematical model because of its key role in describing various processes such as oil reservoir simulations, COVID-19 transmission, mass and energy transport, and global weather production. One of the prominent issues with time fractional differential equations is the design of efficient and stable computational schemes for fast and accurate numerical simulations. We construct in this paper, a simple and yet efficient modified fractional explicit group method (MFEGM) for solving the two-dimensional TFADRE with suitable initial and boundary conditions. The proposed method is established using a difference scheme based on L1 discretization in temporal direction and central difference approximations with double spacing in spatial direction. For comparison purposes, the Crank–Nicolson finite difference method (CNFDM) is proposed. The stability and convergence of the presented methods are theoretically proved and numerically affirmed. We illustrate the computational efficiency of the MFEGM by comparing it to the CNFDM for four numerical examples including fractional diffusion and fractional advection–diffusion models. The numerical results show that the MFEGM is capable of reducing iteration count and CPU timing effectively compared to the CNFDM, making it well-suited to time fractional diffusion equations.

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“…Khan et al [33] considered the numerical approach based on the collocation method for the inverse heat source problem and tasted the method both on regular and irregular domain. Different researchers discussed various numerical approaches for time and space fractionalorder models in the research [27,30,[34][35][36][37][38]. e goal of this research is to propose a new scheme for this model modified implicit scheme for fractional-order RSP-HGSGF.…”

Section: Introductionmentioning

confidence: 99%

The Rayleigh–Stokes Problem for a Heated Generalized Second-Grade Fluid with Fractional Derivative: An Implicit Scheme via Riemann–Liouville Integral

Ganie

Saeed

et al. 2022

Mathematical Problems in Engineering

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The goal of this study is to use the fast algorithm to solve the Rayleigh–Stokes problem for heated generalized second-grade fluid (RSP-HGSGF) with Riemann–Liouville time fractional derivative using the fast algorithm. The modified implicit scheme, which is formulated by the Riemann–Liouville integral formula and applied to the fractional RSP-HGSGF, is proposed. Numerical experiments will be carried out to demonstrate that the scheme is simple to implement, and the results will reveal the best way to implement the suggested technique. The proposed scheme’s stability and convergence will be examined using the Fourier series. The method is stable, and the approximation solution approaches the exact solution. A numerical demonstration will be provided to demonstrate the applicability and viability of the suggested strategy.

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An efficient modified hybrid explicit group iterative method for the time-fractional diffusion equation in two space dimensions

Cited by 17 publications

References 42 publications

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

The Rayleigh–Stokes Problem for a Heated Generalized Second-Grade Fluid with Fractional Derivative: An Implicit Scheme via Riemann–Liouville Integral

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