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- MakaleAçık Erişim2024Scopus SJRQ1A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives
Khan, Zareen A.; Riaz, Muhammad Bilal; Liaqat, Muhammad Imran; Akgül, Ali
Fractional nonlinear partial differential equations are used in many scientific fields to model various processes, although most of these equations lack closed-form solutions. For this reason, methods for approximating solutions that occasionally yield closed-form solutions are crucial for solving these equations. This study introduces a novel technique that combines the residual function and a modified fractional power series with the Elzaki transform to solve various nonlinear problems within the Caputo derivative framework. The accuracy and effectiveness of our approach are validated through analyses of absolute, relative, and residual errors. We utilize the limit principle at zero to identify the coefficients of the series solution terms, while other methods, including variational iteration, homotopy perturbation, and Adomian, depend on integration. In contrast, the residual power series method uses differentiation, and both approaches encounter difficulties in fractional contexts. Furthermore, the effectiveness of our approach in addressing nonlinear problems without relying on Adomian and He polynomials enhances its superiority over various approximate series solution techniques.
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İncele - DüzeltmeAçık Erişim2023Scopus SJRQ1Corrigendum to “Modeling and numerical simulation of non-Newtonian arterial blood flow for mild to severe stenosis” [Alex. Eng. J. 72 (2023) 195–211, (S1110016823002594), (10.1016/j.aej.2023.03.088)]
Nadeem, Sohail; Ali, Shahbaz; Akkurt, Nevzat; Bechir Ben Hamida, Mohamed; Almutairi, Shahah; Ghazwani, Hassan Ali; Eldin, Sayed M.; Khan, Zareen A.; Al-Shafay, A.S.
The authors regards, In the original article, in Ref. [16], the citation was incorrectly stated as: H. Liu et al., 3D printing of artificial blood vessel: study on multi-parameter optimization design for vascular molding effect in alginate and gelatin, Micromachines (2017) 8. However, upon thorough review and verification, the authors have discovered that the correct citation should be as follows: V. Carvalho, N. Rodrigues, R. Ribeiro, P.F. Costa, R.A. Lima, S.F.C.F. Teixeira, 3D printed biomodels for flow visualization in stenotic vessels: An experimental and numerical study, Micromachines, vol. 11, no. 6, doi: 10.3390/mi11060549. The authors deeply apologize for this oversight and any confusion it may have caused to the readers and the scholarly community. It is crucial to ensure the accuracy and integrity of their citations, and they sincerely regret any inconvenience this may have caused.
- MakaleAçık Erişim2023Scopus SJRQ1Modeling and numerical simulation of non-Newtonian arterial blood flow for mild to severe stenosis
Nadeem, Sohail; Ali, Shahbaz; Akkurt, Nevzat; Ben Hamida, Mohamed Bechir; Almutairi, Shahah; Ali Ghazwani, Hassan; Eldin, Sayed M; Khan, Zareen A.; Al-Shafay, A.S.
The fundamental cause of coronary heart disease is thought to be atherosclerosis. Blood flow in arteries under plaque formation is widely studied using both experimental and theoretical methods in literature. This paper presents a comprehensive study on the mathematical modelling and numerical simulation of non-Newtonian blood flow in an idealized stenosed artery. Non-Newtonian behavior of blood flow is assumed by Casson and Quemada fluid models. An analysis is performed for four forms of stenosis, 50%, 60%, 70%, and 80%, which are defined by a narrowing of the artery's diameter. The mathematical model for non-Newtonian fluid transport is presented in the form of highly nonlinear coupled partial differential equations. A finite-volume approach is used to solve the system of equations numerically. The solutions are obtained using a hybrid mesh with hexahedron and tetrahedron control volumes. Numerical solutions are validated first with experimental results from the literature for a Newtonian fluid, and then the results are extended to non-Newtonian fluid models. It can be observed that the non-Newtonian nature of the fluid model influences flow dynamics and is a significant aspect to consider for arteries with small diameter. The velocity and pressure drop rise as the degree of stenosis develops. Wall shear is substantially larger in stenotic passages and severity of stenosis is directly related with this increasing behavior.
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