Üçüncü Mertebeden Kısmi Diferansiyel Denklemin Homotopy Pertürbasyon Metodu ile Çözümü

Modanlı, Mahmut; Eş, Hüseyin

doi:10.17798/bitlisfen.981929

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Fluid mechanics studies complex nonlinear systems that arise in various branches of science and often require simplification of models. On the other hand, research suggests that fractionalorder models may offer more accurate representations of real-life problems compared to integerorder models [7]. Therefore, fractional differential equations have attracted the attention of many researchers in the 21st century.…”

Section: Introductionmentioning

confidence: 99%

Fractional model for blood flow under MHD influence in porous and non-porous media

Ayaz,

Heredağ

2024

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this research, the Magnetohydrodynamic flow model within a porous vessel containing blood was examined. What makes this study intriguing is the inclusion of a fractional-order derivative term in the Magnetohydrodynamic flow system equations. Fractional derivatives were chosen for their ability to encompass both integer and fractional-order derivatives, leading to more realistic modeling results. The numerical solution for the partial differential equation system was obtained using the finite differences method. Solutions were derived using both central difference and backward difference approaches to enhance the reliability of the results. The Grünwald-Letnikov derivative approach was employed for the fractional derivative term, while the Crank-Nicolson method was applied for other terms. Solutions were obtained for velocity, temperature, and concentration profiles. Subsequently, a thorough analysis was conducted to investigate variations in these solutions for changing values of significant flow parameters such as Hartmann number, Grashof number, solute Grashof number, a small positive constant, radiation parameter, Prandtl number, and Schmidt number. Additionally, the study analyzed changes in the fractional derivative order. Finally, the impact of flow parameters on flow in a non-porous medium was investigated, and the results were presented graphically. The study highlighted the significant effects of various parameters on blood flow.

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Section: Introductionmentioning

confidence: 99%

Fractional model for blood flow under MHD influence in porous and non-porous media

Ayaz,

Heredağ

2024

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…[16] tarafından Nanopartiküller sağlayan nanotüplerin dinamik analizinde, 2021'de Modanlı vd. [17] Üçüncü mertebeden kısmi diferansiyel denklemin çözümünde Homotopi yöntemini kullanmıştır.…”

Section: Introductionunclassified

Kesi̇rli̇ Mertebeden Pseudo-Hi̇perboli̇k Kismi̇ Di̇feransi̇yel Denklemi̇ni̇n Homotopi̇ Pertürbasyon Yöntemi̇yle Yaklaşik Çözümü

Çiçek

Modanlı

2022

Uşak Üniversitesi Fen Ve Doğa Bilimleri Dergisi

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Bu çalışmada başlangıç değerlere bağlı kesirli mertebeden (Fractional order) Pseudo-Hiperbolik kısmi diferansiyel denkleminin homotopi pertürbasyon metoduyla çözümü incelenecektir. Kesirli mertebeden Pseoudo-Hiperbolik kısmi diferansiyel denkleminin farklı yöntemlerle çözümü mevcut olmasına rağmen homotopi pertürbasyon yöntemiyle çözümü daha kısa ve hata payı daha az olduğundan çözüm bu yöntemle yapılmıştır. Ayrıca Matlab programı yardımıyla tam çözüm grafik ile görselleştirilmiştir.

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Numerical Solutions of Fractional Order Pseudo Hyperbolic Differential Equations by Finite Difference Method

Ozbag

Modanlı

2022

Afyon Kocatepe University Journal of Sciences and Engineering

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Fractional differential equations are useful for modelling mathematical issues in fields including engineering, physics, and biology. In this article, approximate solutions of an initial boundary value problem for fractional pseudo hyperbolic differential equations are investigated using the finite difference method. First, a first-order finite difference scheme is created for the initial boundary value problem. Then, stability analysis was performed for this finite difference scheme. In order to support the theoretical results obtained, error values were calculated for precise and approximate solutions in different fractional order derivatives of a sample problem. Some numerical simulations are also given to show the effectiveness of the applied solution method.

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Üçüncü Mertebeden Kısmi Diferansiyel Denklemin Homotopy Pertürbasyon Metodu ile Çözümü

Cited by 3 publications

References 17 publications

Fractional model for blood flow under MHD influence in porous and non-porous media

Fractional model for blood flow under MHD influence in porous and non-porous media

Kesi̇rli̇ Mertebeden Pseudo-Hi̇perboli̇k Kismi̇ Di̇feransi̇yel Denklemi̇ni̇n Homotopi̇ Pertürbasyon Yöntemi̇yle Yaklaşik Çözümü

Numerical Solutions of Fractional Order Pseudo Hyperbolic Differential Equations by Finite Difference Method

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