Yıl 2020,
Cilt: 3 Sayı: 1, 203 - 206, 15.12.2020
Ulviye Demirbilek
,
Volkan Ala
Khanlar R. Mamedov
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.
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.