Computational analysis of time-fractional models in energy infrastructure applications

Ahmad, Imtiaz; Bakar, Asmidar Abu; Ali, Ihteram; Haq, Sirajul; Yussof, Salman; Ali, Ali Hasan

doi:10.1016/j.aej.2023.09.057

Cited by 15 publications

(3 citation statements)

References 73 publications

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“…Consequently, there has been a significant focus on developing approximate analytical solutions for FDEs, becoming a prominent area of interest in both academic research and practical applications. The application of fractional calculus has proven beneficial in modeling and control theory across a diverse array of fields [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Exploring fractional-order new coupled Korteweg-de Vries system via improved Adomian decomposition method

Arshad,

Aldosary,

Batool

et al. 2024

PLoS ONE

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This paper aims to extend the applications of the projected fractional improved Adomian Decomposition method (fIADM) to the fractional order new coupled Korteweg-de Vries (cKdV) system. This technique is significantly recognized for its effectiveness in addressing nonlinearities and iteratively handling fractional derivatives. The approximate solutions of the fractional-order new cKdV system are obtained by employing the improved ADM in fractional form. These solutions play a crucial role in designing and optimizing systems in engineering applications where accurate modeling of wave phenomena is essential, including fluid dynamics, plasma physics, nonlinear optics, and other mathematical physics domains. The fractional order new cKdV system, integrating fractional calculus, enhances accuracy in modeling wave interactions compared to the classical cKdV system. Comparison with exact solutions demonstrates the high accuracy and ease of application of the projected method. This proposed technique proves influential in resolving fractional coupled systems encountered in various fields, including engineering and physics. Numerical results obtained using Mathematica software further verify and demonstrate its efficacy.

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Section: Introductionmentioning

confidence: 99%

Exploring fractional-order new coupled Korteweg-de Vries system via improved Adomian decomposition method

Arshad,

Aldosary,

Batool

et al. 2024

PLoS ONE

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“…Notably, novel methodologies for solving time-dependent PDEs were proposed by combining hybrid Fibonacci and Lucas polynomial schemes [47,48]. Moreover, researchers employed finite differences and Lucas polynomials to achieve effective numerical solutions for various PDE models [49,50].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo–Lucas–Fibonacci Approach with Strang Splitting

Ahmad,

Alshammari,

Jan

et al. 2024

Fractal Fract

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The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville–Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources.

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“…Notably, RBF based MM have emerged as a prominent sub-type. These methods employ mathematical functions to effectively interpolate data values at scattered points, providing reliable approximations for solving PDEs [34][35][36][37][38][39]. RBF-based meshless methods offer a significant benefit in terms of their ease of implementation and adaptability to handle problems involving irregular geometries.…”

Section: Introductionmentioning

confidence: 99%

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater

Ahmad,

Ali,

Jan

et al. 2023

PLoS ONE

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The study presents a meshless computational approach for simulating the three-dimensional multi-term time-fractional mobile-immobile diffusion equation in the Caputo sense. The methodology combines a stable Crank-Nicolson time-integration scheme with the definition of the Caputo derivative to discretize the problem in the temporal direction. The spatial function derivative is approximated using the inverse multiquadric radial basis function. The solution is approximated on a set of scattered or uniform nodes, resulting in a sparse and well-conditioned coefficient matrix. The study highlights the advantages of meshless method, particularly their simplicity of implementation in higher dimensions. To validate the accuracy and efficacy of the proposed method, we performed numerical simulations and compared them with analytical solutions for various test problems. These simulations were carried out on computational domains of both rectangular and non-rectangular shapes. The research highlights the potential of meshless techniques in solving complex diffusion problems and its successful applications in groundwater contamination and other relevant fields.

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Computational analysis of time-fractional models in energy infrastructure applications

Cited by 15 publications

References 73 publications

Exploring fractional-order new coupled Korteweg-de Vries system via improved Adomian decomposition method

Exploring fractional-order new coupled Korteweg-de Vries system via improved Adomian decomposition method

An Efficient Numerical Solution of a Multi-Dimensional Two-Term Fractional Order PDE via a Hybrid Methodology: The Caputo–Lucas–Fibonacci Approach with Strang Splitting

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater

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