KESİRLİ MERTEBEDEN PSEUDO-HİPERBOLİK KISMİ DİFERANSİYEL DENKLEMİNİN HOMOTOPİ PERTÜRBASYON YÖNTEMİYLE YAKLAŞIK ÇÖZÜMÜ

Year 2022, Volume: 6 Issue: 2, 67 - 75, 29.12.2022

Harun Çiçek Mahmut Modanlı

https://doi.org/10.47137/usufedbid.1137666

Abstract

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.

Keywords

Kesirli mertebe, Pseoudo-Hiperbolik denklem, homotopi p pertürbasyon metodu, Tam çözüm, Yaklaşık çözüm

APROXIMATE SOLUTION OF FRACTIONAL-ORDER PSEUDO-HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION BY HOMOTOPY PERTURBATION METHOD

Abstract

In this study, the solution of Fractional order Pseudo-Hyperbolic partial differential equation with initial conditions will be examined by homotopy perturbation method. Although the fractional Pseoudo-Hyperbolic partial differential equation has a solution with different methods, the solution is made with this method, since its solution is shorter and the margin of error is less with the homotopy perturbation method. In addition, with the help of Matlab program, the full solution was visualized with graphics.

Keywords

Fractional order, Pseudo-Hyperbolic equation, homotopy p perturbation method, Exact solution, Approximate solution

References

• [1] J. Lıu, ve G. Hou,, Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method, Applied Mathematics and Computation, 2011,217 (16): 7001–7008.
• [2] S. Momanı, ve Z. Odıbat,, Analytical solution of a time-fractional Navier–Stokes equation by Adomian decomposition method, Applied Mathematics and Computation, 2006, 177(2): 488–494.
• [3] M. G. Sakar, ve F. Erdogan,, The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition method, Applied Mathematical Modelling, 2013, 37(20-21): 8876–8885.
• [4] B. Zubik-Kowal, Chebyshev pseudospectral method and waveform relaxation for differential and differential-functional parabolic equations. Applied Numerical Mathematics, 2000, 34(2-3): 309–328. [5] S. Kumar, D. Kumar, Abbasbandy, S., ve Rashıdı, M. M., Analytical solution of fractional Navier-Stokes equation by using modified Laplace decomposition method, Ain Shams Engineering Journal, 2014, 5(2): 569–574.
• [6] S. Kumar, A. Yıldırım, Y. Khan, H. Jafarı, K. Sayevand, ve L. Weı, Analytical solution of fractional Black-Scholes European option pricing equation by using Laplace transform, Journal of Fractional Calculus and Applications, 2012, 2(8): 1-9.
• [7] J. Tanthanuch, Symmetry analysis of the nonhomogeneous inviscid Burgers equation with delay, Communications in Nonlinear Science and Numerical Simulation, 2012, 17(12): 4978–4987.
• [8] M. Kurulay, The approximate and exact solutions of the space and time-fractional Burggres equations, International Journal of Research and Reviews in Applied Sciences, 2010, 3(3): 257–263.
• [9] S.T. Abdulazeez ve M. Modanlı, olutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method, Alexandria Engineering Journal, 2022, 61(12):12443-12451.
• [10] M. Modanlı, S.T. Abdulazeez ve A.M. Husien, A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions, Numer Methods Partial Differential Eq., 2021, 37: 2235–2243.
• [11] W.M. Osman, T.M. Elzaki ve N.A.A. Siddig, Modified Double Conformable Laplace Transform and Singular Fractional Pseudo-Hyperbolic and Pseudo-Parabolic Equations, Journal of King Saud University – Science, 2021, 33 (2021): 101378.
• [12] I. Fedotov, M. Shatalov, ve J. Marais, Hyperbolic and pseudo-hyperbolic equations in the theory of vibration, ActaMech 2016, 227 :3315–3324.
• [13] Chavan S. S., Panchal M. M., Solution of third order Korteweg-De Vries equation by homotopy perturbation method using Elzaki transform. Int J Res Appl Sci Eng Tech., 2014, 2:366-9.
• [14] He J. H., El-Dib Y. O., Mady A. A., Homotopy perturbation method for the fractal Toda oscillator. Fractal and Fractional, 2021, 5 (3): 93.
• [15] Karimiasl M., Ebrahimi F., Mahesh V., Postbuckling analysis of piezoelectric multiscale sandwich composite doubly curved porous shallow shells via Homotopy Perturbation Method. Engineering with Computers, 2021, 37 (1): 561-577.
• [16] Rezapour B., Fariborzi Araghi M. A., Vázquez-Leal H., Application of homotopy perturbation method for dynamic analysis of nanotubes delivering nanoparticles. Journal of Vibration and Control, 2021, 27 (7-8): 802-814.
• [17] M. Modanlı ve H. Eş, , Üçüncü Mertebeden Kısmi Diferansiyel Denklemin Homotopy Pertürbasyon Metodu ile Çözümü, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi (BEU Journal of Science), 2021, 10 (4): 1527-1534.