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Yıl 2020, Cilt: 3 Sayı: 1, 203 - 206, 15.12.2020

Ulviye Demirbilek Volkan Ala Khanlar R. Mamedov

Öz

Kaynakça

  • 1 A. Emad, B. Abdel-Salam , A. Y. Eltayeb, Solution of nonlinear space-time fractional differential equations using the fractional Riccati expansion method, Math. Probl. Eng., 2013 (2013), Article ID 846283, doi: 10.1155 2013 846283.
  • 2 W. Liu, K. Chen, The functional variable method for finding exact solutions of some nonlinear time fractional differential equations, Pramana, 81 (2013), 377-384.
  • 3 Z. Bin , Exp-function method for solving fractional partial diferential equations, The Sci. World J., 2013 (2013), Article ID 465723, doi:10.1155/2013/465723.
  • 4 B. Lu, The first integral method for some time fractional differential equations, J. Math. Anal. Appl., 395 (2012) , 684-693.
  • 5 V. Ala, U. Demirbilek, Kh. R. Mamedov, An Application of Improved Bernoulli Sub-Equation Function Method to the Nonlinear conformable Time Fractional SRLW Equation, AIMS Mathematics, 5(4) (2020), 3751-3761.
  • 6 J. Boussinesq, Essai sur la theorie des eaux courantes, Memoires presentes par divers savants l Acad. des Sci. Inst. Nat. France, XXIII, (1877) 1-680.
  • 7 D. J. Korteweg, G. de Vries, On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves, Phil. Mag., 39 (240) (1895), 422-443.
  • 8 M. Wadati, M. Toda , The Exact N-soliton solution of the Korteweg-de Vries Equation, Journal of Phy. Soc. of Japan, 32 (5) (1972) , 1403-1411.
  • 9 R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Letters, 27(18) (1971), 1192.
  • 10 D. Zheng-De, L. Zhen-Jiang, L. Dong-Long, Exact periodic solitary-wave solution for KdV equation, Chinese Phy. L., 25(5) (2008), 1531.
  • 11 A. Korkmaz, Complex wave solutions to mathematical biology models I: Newell-Whitehead-Segel and Zeldovich equations, Journal of Comput. and Non. Dyn., 13 (8) (2018), 081004. 12 M. S. Osman, A., H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, The unified method for conformable time fractional Schrodinger equation with perturbation terms, Chin. J. Phy. Physics, 56(5) (2018), 2500-2506.
  • 13 R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., Pramana, 264 (2014), 65-70.
  • 14 T. Abdeljawad, On Conformable Fractional Calculus, J. Comput. Appl. Math., 279 (2015), 57-66.
  • 15 K. Hosseini, R. Ansari,New exact solutions of nomlinear conformable time- fractional Boussinesq equations using the modified Kudryashov method, Waves in R. and Comp. Media, 27 (4) (2017), 628-636.
  • 16 A. Zafar, Rational exponential solutions of conformable space-time fractional equal-width equations, Nonlinear Engineering, 8(1) (2019), 350-355.
  • 17 H. Bulut , H.M. Baskonus, Exponential prototype structures for (2 + 1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics, Waves in R. and Comp. Media, 26(2) (2016), 189-195.
  • 18 U. Demirbilek , V. Ala , Kh. R. Mamedov, S. Goktas, On the exact solution of fractional Simplified MCH Equation, Sovremennie problemi teoriya funkchii i ix prilojeniya, Saratov, (2020), 150-152.
  • 19 F. Dusunceli, E. Celik, M. Askin, H. Bulut, New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method, Indian J. of Phy.,(2020) doi:10.1007/s12648-020-01707-5.
  • 20 F. Dusunceli, New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model, Adv.in Math. Phy., (2019), doi:/10.1155/2019/7801247.

On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM

Yıl 2020, Cilt: 3 Sayı: 1, 203 - 206, 15.12.2020

Ulviye Demirbilek Volkan Ala Khanlar R. Mamedov

Öz

Investigating the solutions of fractional differential equations are essential to understand the nonlinear process that appears in some branch of physical phenomena such as optics, quantum electrons, control theory of dynamical systems. Several computational techniques for the solutions of these equations have been developed. In this study, we implement the Improved Bernoulli Sub-Equation Function Method (IBSEFM) to construct the exact solutions of conformable time fractional KdV equation. We obtain new travelling wave solutions of KdV equation via IBSEFM. We plot the contourplots and 2D,3D graphs by the aid of mathematics software that acquired from the values of the solutions.

Anahtar Kelimeler

Conformable Time Fractional Derivative Exact Solutions Improved Bernoulli Sub-Equation Funtion Method

Kaynakça

  • 1 A. Emad, B. Abdel-Salam , A. Y. Eltayeb, Solution of nonlinear space-time fractional differential equations using the fractional Riccati expansion method, Math. Probl. Eng., 2013 (2013), Article ID 846283, doi: 10.1155 2013 846283.
  • 2 W. Liu, K. Chen, The functional variable method for finding exact solutions of some nonlinear time fractional differential equations, Pramana, 81 (2013), 377-384.
  • 3 Z. Bin , Exp-function method for solving fractional partial diferential equations, The Sci. World J., 2013 (2013), Article ID 465723, doi:10.1155/2013/465723.
  • 4 B. Lu, The first integral method for some time fractional differential equations, J. Math. Anal. Appl., 395 (2012) , 684-693.
  • 5 V. Ala, U. Demirbilek, Kh. R. Mamedov, An Application of Improved Bernoulli Sub-Equation Function Method to the Nonlinear conformable Time Fractional SRLW Equation, AIMS Mathematics, 5(4) (2020), 3751-3761.
  • 6 J. Boussinesq, Essai sur la theorie des eaux courantes, Memoires presentes par divers savants l Acad. des Sci. Inst. Nat. France, XXIII, (1877) 1-680.
  • 7 D. J. Korteweg, G. de Vries, On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves, Phil. Mag., 39 (240) (1895), 422-443.
  • 8 M. Wadati, M. Toda , The Exact N-soliton solution of the Korteweg-de Vries Equation, Journal of Phy. Soc. of Japan, 32 (5) (1972) , 1403-1411.
  • 9 R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Letters, 27(18) (1971), 1192.
  • 10 D. Zheng-De, L. Zhen-Jiang, L. Dong-Long, Exact periodic solitary-wave solution for KdV equation, Chinese Phy. L., 25(5) (2008), 1531.
  • 11 A. Korkmaz, Complex wave solutions to mathematical biology models I: Newell-Whitehead-Segel and Zeldovich equations, Journal of Comput. and Non. Dyn., 13 (8) (2018), 081004. 12 M. S. Osman, A., H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, The unified method for conformable time fractional Schrodinger equation with perturbation terms, Chin. J. Phy. Physics, 56(5) (2018), 2500-2506.
  • 13 R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., Pramana, 264 (2014), 65-70.
  • 14 T. Abdeljawad, On Conformable Fractional Calculus, J. Comput. Appl. Math., 279 (2015), 57-66.
  • 15 K. Hosseini, R. Ansari,New exact solutions of nomlinear conformable time- fractional Boussinesq equations using the modified Kudryashov method, Waves in R. and Comp. Media, 27 (4) (2017), 628-636.
  • 16 A. Zafar, Rational exponential solutions of conformable space-time fractional equal-width equations, Nonlinear Engineering, 8(1) (2019), 350-355.
  • 17 H. Bulut , H.M. Baskonus, Exponential prototype structures for (2 + 1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics, Waves in R. and Comp. Media, 26(2) (2016), 189-195.
  • 18 U. Demirbilek , V. Ala , Kh. R. Mamedov, S. Goktas, On the exact solution of fractional Simplified MCH Equation, Sovremennie problemi teoriya funkchii i ix prilojeniya, Saratov, (2020), 150-152.
  • 19 F. Dusunceli, E. Celik, M. Askin, H. Bulut, New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method, Indian J. of Phy.,(2020) doi:10.1007/s12648-020-01707-5.
  • 20 F. Dusunceli, New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model, Adv.in Math. Phy., (2019), doi:/10.1155/2019/7801247.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Ulviye Demirbilek

Volkan Ala Bu kişi benim

Khanlar R. Mamedov Bu kişi benim

Yayımlanma Tarihi 15 Aralık 2020
Kabul Tarihi 29 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Demirbilek, U., Ala, V., & Mamedov, K. R. (2020). On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM. Conference Proceedings of Science and Technology, 3(1), 203-206.
AMA Demirbilek U, Ala V, Mamedov KR. On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM. Conference Proceedings of Science and Technology. Aralık 2020;3(1):203-206.
Chicago Demirbilek, Ulviye, Volkan Ala, ve Khanlar R. Mamedov. “On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM”. Conference Proceedings of Science and Technology 3, sy. 1 (Aralık 2020): 203-6.
EndNote Demirbilek U, Ala V, Mamedov KR (01 Aralık 2020) On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM. Conference Proceedings of Science and Technology 3 1 203–206.
IEEE U. Demirbilek, V. Ala, ve K. R. Mamedov, “On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM”, Conference Proceedings of Science and Technology, c. 3, sy. 1, ss. 203–206, 2020.
ISNAD Demirbilek, Ulviye vd. “On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM”. Conference Proceedings of Science and Technology 3/1 (Aralık 2020), 203-206.
JAMA Demirbilek U, Ala V, Mamedov KR. On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM. Conference Proceedings of Science and Technology. 2020;3:203–206.
MLA Demirbilek, Ulviye vd. “On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM”. Conference Proceedings of Science and Technology, c. 3, sy. 1, 2020, ss. 203-6.
Vancouver Demirbilek U, Ala V, Mamedov KR. On the Exact Solutions of a Nonlinear Conformable Time Fractional Equation via IBSEFM. Conference Proceedings of Science and Technology. 2020;3(1):203-6.
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