2022
DOI: 10.1007/978-3-031-04812-8_9
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Variational Method for Solving the Time-Fractal Heat Conduction Problem in the Claydite-Block Construction

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Cited by 8 publications
(12 citation statements)
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“…Consequently, employing the homotopy analysis method to derive analytic solutions for the model [46,47] may enhance the sensitivity analysis, as these analytic solutions could potentially reduce computational expenses. Furthermore, it may be of interest to conduct a research study aimed at developing a computational tool for numerically solving the model, based on the methods proposed in the referenced papers [42,43]. In addition, addressing the positivity of the solutions of the model is an important consideration [48].…”
Section: Discussionmentioning
confidence: 99%
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“…Consequently, employing the homotopy analysis method to derive analytic solutions for the model [46,47] may enhance the sensitivity analysis, as these analytic solutions could potentially reduce computational expenses. Furthermore, it may be of interest to conduct a research study aimed at developing a computational tool for numerically solving the model, based on the methods proposed in the referenced papers [42,43]. In addition, addressing the positivity of the solutions of the model is an important consideration [48].…”
Section: Discussionmentioning
confidence: 99%
“…However, the convergence and accuracy of this method have not yet been evaluated. Recently, novel numerical methods have been developed to solve fractional-order ordinary differential equations efficiently, and their analyses have yielded several interesting results [42,43]. The employment of these methods in creating a new Python solver for fractional-order ordinary differential equations could lead to intriguing research opportunities.…”
Section: Numerical Methods For Solving the Fractional Differential Eq...mentioning
confidence: 99%
“…In this section, we shall prove the existence and uniqueness for the MFE scheme (5)- (6). We first give some lemmas, which are important in subsequent theoretical analysis.…”
Section: Existence and Uniquenessmentioning
confidence: 99%
“…Noting that u 0 h , λ 0 h = (R h u 0 , R h λ 0 ), we have θ 0 = 0 and η 0 = 0. We next give the convergence results for the MFE scheme ( 5)- (6).…”
Section: Now We Write the Errorsmentioning
confidence: 99%
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