Araştırma Makalesi
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Yıl 2020, Cilt: 3 Sayı: 2, 61 - 68, 22.06.2020

Emrah Atilgan Orkun Taşbozan Ali Kurt Syed Tauseef Mohyud-din

Öz

Kaynakça

  • [1] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [2] A. A. Kilbas , H. M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
  • [3] K.S. Miller, B. Ross ,An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.
  • [4] R. Khalil, M. A. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.
  • [5] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66.
  • [6] W.S. Chung, Fractional Newton mechanics with conformable fractional derivative, J. Comput. Appl. Math., 290 (2015), 150-158.
  • [7] A. Neirameh, New fractional calculus and application to the fractional-order of extended biological population model, Bol. da Soc. Parana. Matematica, 36(3)(2018), 115.
  • [8] N. Benkhettou, S. Hassani, D. F. M. Torres, A conformable fractional calculus on arbitrary time scales, J. King Saud Univ. - Sci., 28(1) (2016), 93-98.
  • [9] D. Zhao and T. Li, On conformable delta fractional calculus on time scales, J. Math. Comput. Sci., 16 (2016), 324-335.
  • [10] M. Eslami, H. Rezazadeh, The First integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo, 53(3) (2016), 475-485.
  • [11] M. A. El-Tawil, S. N. Huseen, The Q-homotopy analysis method (Q-HAM ), Int. J. Appl. Math. Mech., 8(15)(2012), 51-75.
  • [12] S. J. Liao, The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems, Shanghai Jiao Tong University, 1992.
  • [13] O. S. Iyiola, M. E. Soh, C. D. Enyi, Generalised homotopy analysis method (q-HAM) for solving foam drainage equation of time fractional type, Math. Eng. Sci. Aerosp., 4(4)(2013), 429-440.
  • [14] O. S. Iyiola, F. D. Zaman, A fractional diffusion equation model for cancer tumor, AIP Adv., 4(10)(2014), 107121.
  • [15] A. Korkmaz, Explicit exact solutions to some one-dimensional conformable time fractional equations, Waves Random Complex Media (2017), 1-14.
  • [16] K. Hosseini, A. Bekir, M. Kaplan, O. Guner, On a new technique for solving the nonlinear conformable time-fractional differential equations, Opt. Quant. Electron. (2017) 49-343.
  • [17] P. A. Naik, J. Zu, J., M. Ghoreishi, Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method, Chaos Solitons Fractals (2019), 109500.
  • [18] M. Ghoreishi, A. I. B. Md.Ismail, A. K. Alomari, A.S. Batainehc, The comparison between homotopy analysis method and optimal homotopy asymptotic method for nonlinear age-structured population models, Commun. Nonlinear Sci. Numer. Simul., 17(3)(2012),1163-1177.
  • [19] M. Yavuz, Novel solution methods for initial boundary value problems of fractional order with conformable differentiation, Int. J. Optim. Control. Theor. Appl. IJOCTA, 8(1) (2017), 1-7.
  • [20] M. Ghoreishi, A. M. Ismail, A. K. Alomari, Comparison between homotopy analysis method and optimal homotopy asymptotic method for nth-order integro-differential equation, Math. Methods Appl. Sci., 34(15) (2011), 1833-1842.

Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker's Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation

Yıl 2020, Cilt: 3 Sayı: 2, 61 - 68, 22.06.2020

Emrah Atilgan Orkun Taşbozan Ali Kurt Syed Tauseef Mohyud-din

Öz

In this paper, we propose the approximate analytical solutions of conformable time fractional Clannish Random Walker's Parabolic(CRWP) equation and Modified Benjamin-Bona-Mahony(BBM) equation with the aid of generalized homotopy analysis method (q-HAM). The $h$ curves of approximate solutions for both equations are illustrated by graphics to determine the convergence interval. $h$ values obtained from these graphics are used to compare approximate solutions with the analytical solutions. The results show that approximate solutions are consistent with the analytical solutions. Also it is understood that the method is reliable, applicable and efficient technique to get the exact solutions of fractional partial differential equations.

Anahtar Kelimeler

Fractional Clannish Random Walker's Parabolic(CRWP) Equation Modi ed Benjamin-Bona-Mahony(BBM) equation Conformable Derivative

Kaynakça

  • [1] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [2] A. A. Kilbas , H. M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
  • [3] K.S. Miller, B. Ross ,An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.
  • [4] R. Khalil, M. A. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.
  • [5] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66.
  • [6] W.S. Chung, Fractional Newton mechanics with conformable fractional derivative, J. Comput. Appl. Math., 290 (2015), 150-158.
  • [7] A. Neirameh, New fractional calculus and application to the fractional-order of extended biological population model, Bol. da Soc. Parana. Matematica, 36(3)(2018), 115.
  • [8] N. Benkhettou, S. Hassani, D. F. M. Torres, A conformable fractional calculus on arbitrary time scales, J. King Saud Univ. - Sci., 28(1) (2016), 93-98.
  • [9] D. Zhao and T. Li, On conformable delta fractional calculus on time scales, J. Math. Comput. Sci., 16 (2016), 324-335.
  • [10] M. Eslami, H. Rezazadeh, The First integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo, 53(3) (2016), 475-485.
  • [11] M. A. El-Tawil, S. N. Huseen, The Q-homotopy analysis method (Q-HAM ), Int. J. Appl. Math. Mech., 8(15)(2012), 51-75.
  • [12] S. J. Liao, The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems, Shanghai Jiao Tong University, 1992.
  • [13] O. S. Iyiola, M. E. Soh, C. D. Enyi, Generalised homotopy analysis method (q-HAM) for solving foam drainage equation of time fractional type, Math. Eng. Sci. Aerosp., 4(4)(2013), 429-440.
  • [14] O. S. Iyiola, F. D. Zaman, A fractional diffusion equation model for cancer tumor, AIP Adv., 4(10)(2014), 107121.
  • [15] A. Korkmaz, Explicit exact solutions to some one-dimensional conformable time fractional equations, Waves Random Complex Media (2017), 1-14.
  • [16] K. Hosseini, A. Bekir, M. Kaplan, O. Guner, On a new technique for solving the nonlinear conformable time-fractional differential equations, Opt. Quant. Electron. (2017) 49-343.
  • [17] P. A. Naik, J. Zu, J., M. Ghoreishi, Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method, Chaos Solitons Fractals (2019), 109500.
  • [18] M. Ghoreishi, A. I. B. Md.Ismail, A. K. Alomari, A.S. Batainehc, The comparison between homotopy analysis method and optimal homotopy asymptotic method for nonlinear age-structured population models, Commun. Nonlinear Sci. Numer. Simul., 17(3)(2012),1163-1177.
  • [19] M. Yavuz, Novel solution methods for initial boundary value problems of fractional order with conformable differentiation, Int. J. Optim. Control. Theor. Appl. IJOCTA, 8(1) (2017), 1-7.
  • [20] M. Ghoreishi, A. M. Ismail, A. K. Alomari, Comparison between homotopy analysis method and optimal homotopy asymptotic method for nth-order integro-differential equation, Math. Methods Appl. Sci., 34(15) (2011), 1833-1842.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Emrah Atilgan Bu kişi benim 0000-0002-0395-9976

Orkun Taşbozan 0000-0001-5003-6341

Ali Kurt 0000-0002-0617-6037

Syed Tauseef Mohyud-din 0000-0002-0442-7883

Yayımlanma Tarihi 22 Haziran 2020
Gönderilme Tarihi 22 Ekim 2019
Kabul Tarihi 3 Haziran 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 2

Kaynak Göster

APA Atilgan, E., Taşbozan, O., Kurt, A., Mohyud-din, S. T. (2020). Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation. Universal Journal of Mathematics and Applications, 3(2), 61-68.
AMA Atilgan E, Taşbozan O, Kurt A, Mohyud-din ST. Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation. Univ. J. Math. Appl. Haziran 2020;3(2):61-68.
Chicago Atilgan, Emrah, Orkun Taşbozan, Ali Kurt, ve Syed Tauseef Mohyud-din. “Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) Equation”. Universal Journal of Mathematics and Applications 3, sy. 2 (Haziran 2020): 61-68.
EndNote Atilgan E, Taşbozan O, Kurt A, Mohyud-din ST (01 Haziran 2020) Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation. Universal Journal of Mathematics and Applications 3 2 61–68.
IEEE E. Atilgan, O. Taşbozan, A. Kurt, ve S. T. Mohyud-din, “Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation”, Univ. J. Math. Appl., c. 3, sy. 2, ss. 61–68, 2020.
ISNAD Atilgan, Emrah vd. “Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) Equation”. Universal Journal of Mathematics and Applications 3/2 (Haziran 2020), 61-68.
JAMA Atilgan E, Taşbozan O, Kurt A, Mohyud-din ST. Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation. Univ. J. Math. Appl. 2020;3:61–68.
MLA Atilgan, Emrah vd. “Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) Equation”. Universal Journal of Mathematics and Applications, c. 3, sy. 2, 2020, ss. 61-68.
Vancouver Atilgan E, Taşbozan O, Kurt A, Mohyud-din ST. Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation. Univ. J. Math. Appl. 2020;3(2):61-8.
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