Browse Journals

[1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015), 57-66.

DOI: https://doi.org/10.1016/j.cam.2014.10.016

[2] H. M. Baskonus and J. F. Gómez-Aguilar, New singular soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod with M-derivative, Modern Physics Letters B 33(21) (2019); Article 1950251.

DOI: https://doi.org/10.1142/S0217984919502518

[3] N. Benkhettou, S. Hassani and D. F. M. Torres, A conformable fractional calculus on arbitrary time scales, Journal of King Saud University - Science 28(1) (2016), 93-98.

DOI: https://doi.org/10.1016/j.jksus.2015.05.003

[4] F. E. Benth and J. Gjerde, A remark on the equivalence between Poisson and Gaussian stochastic partial differential equations, Potential Analysis 8(2) (1998), 179-193.

DOI: https://doi.org/10.1023/A:1008649128307

[5] Y. Cenesiz, D. Baleanu, A. Kurt and O. Tasbozan, New exact solutions of Burgers’ type equations with conformable derivative, Waves in Random and Complex Media 27(1) (2017), 103-116.

DOI: https://doi.org/10.1080/17455030.2016.1205237

[6] W. S. Chung, Fractional Newton mechanics with conformable fractional derivative, Journal of Computational and Applied Mathematics 290 (2015), 150-158.

DOI: https://doi.org/10.1016/j.cam.2015.04.049

[7] V. Daftardar-Gejji and H. Jafari, Solving a multi-order fractional differential equation using adomian decomposition, Applied Mathematics and Computation 189(1) (2007), 541-548.

DOI: https://doi.org/10.1016/j.amc.2006.11.129

[8] V. Daftardar-Gejji and S. Bhalekar, Solving multi-term linear and non-linear diffusion–wave equations of fractional order by Adomian decomposition method, Applied Mathematics and Computation 202(1) (2008), 113-120.

DOI: https://doi.org/10.1016/j.amc.2008.01.027

[9] M. Eslami and H. Rezazadeh, The first integral method for Wu–Zhang system with conformable time-fractional derivative, Calcolo 53(3) (2016), 475-485.

DOI: https://doi.org/10.1007/s10092-015-0158-8

[10] Z. Z. Ganji, D. D. Ganji and Y. Rostamiyan, Solitary wave solutions for a time-fraction generalized Hirota–Satsuma coupled KdV equation by an analytical technique, Applied Mathematical Modelling 33(7) (2009), 3107-3113.

DOI: https://doi.org/10.1016/j.apm.2008.10.034

[11] B. Ghanbari and J. F. Gómez-Aguilar, Optical soliton solutions of the Ginzburg-Landau equation with conformable derivative and Kerr law nonlinearity, Revista Mexicana de Física 65(1) (2019), 73-81.

DOI: https://doi.org/10.31349/RevMexFis.65.73

[12] B. Ghanbari and J. F. Gómez-Aguilar, Optical soliton solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation, Modern Physics Letters B 33(32) (2019); Article 1950402.

DOI: https://doi.org/10.1142/S0217984919504025

[13] H. A. Ghany, Exact solutions for stochastic generalized Hirota-Satsuma coupled KdV equations, Chinese Journal of Physics 49(4) (2011), 926-940.

[14] H. A. Ghany, Exact solutions for stochastic fractional Zakharov-Kuznetsov equations, Chinese Journal of Physics 51(5) (2013), 875-881.

DOI: https://doi.org/10.6122/CJP.51.875

[15] H. A. Ghany, Analytical approach to exact solutions for the wick-type stochastic space-time fractional KdV equation, Chinese Physics Letters 31(6) (2014); Article 060503.

DOI: https://doi.org/10.1088/0256-307X/31/6/060503

[16] H. A. Ghany and A. Hyder, White noise functional solutions for the wick-type two-dimensional stochastic Zakharov-Kuznetsov equations, International Review of Physics 6(2) (2012), 153-157.

[17] H. A. Ghany and A. Hyder, Local and global well-posedness of stochastic Zakharov-Kuznetsov equation, Journal of Computational Analysis and Applications 15(7) (2013), 1332-1343.

[18] H. A. Ghany and A. Hyder, Exact solutions for the wick-type stochastic time-fractional KdV equations, Kuwait Journal of Science 41(1) (2014), 75-84.

[19] H. A. Ghany and A. Hyder and M. Zakarya, Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives, Chinese Physics B 29(3) (2020); Article 030203.

DOI: https://doi.org/10.1088/1674-1056/ab75c9

[20] H. A. Ghany and M. S. Mohammed, White noise functional solutions for wick-type stochastic fractional KdV-Burgers-Kuramoto equations, Chinese Journal of Physics 50(4) (2012), 619-627.

[21] H. A. Ghany, A. S. Okb El Bab, A. M. Zabel and A. Hyder, The fractional coupled KdV equations: Exact solutions and white noise functional approach, Chinese Physics B 22(8) (2013); Article 080501.

DOI: https://doi.org/10.1088/1674-1056/22/8/080501

[22] A. GökdoÄŸan, E Ünal and E. Çelik, Existence and uniqueness theorems for sequential linear conformable fractional differential equations, Miskolc Mathematical Notes 17(1) (2016), 267-279.

DOI: https://doi.org/10.18514/MMN.2016.1635

[23] A. Golbabai and K. Sayevand, The homotopy perturbation method for multi-order time fractional differential equations, Nonlinear Science Letters A 1 (2010), 147-154.

[24] A. Golbabai and K. Sayevand, Analytical treatment of differential equations with fractional coordinate derivatives, Computers & Mathematics with Applications 62(3) (2011), 1003-1012.

DOI: https://doi.org/10.1016/j.camwa.2011.03.047

[25] M. A. Hammad and R. Khalil, Conformable Fractional Heat Differential Equation, International Journal of Pure and Applied Mathematics 94(2) (2014), 215-221.

DOI: https://doi.org/10.12732/ijpam.v94i2.8

[26] J.-H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics 35(1) (2000), 37-43.

DOI: https://doi.org/10.1016/S0020-7462(98)00085-7

[27] J. H. He, S. K. Elagan and Z. B. Li, Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus, Physics Letters A 376(4) (2012), 257-259.

DOI: https://doi.org/10.1016/j.physleta.2011.11.030

[28] W. Hereman, Shallow Water Waves and Solitary Waves, Encyclopedia of Complexity and Systems Science, Editor R. A. Meyers, Springer Verlag, Heibelberg, Germany, 2009, pp.1620-1536.

DOI: https://doi.org/10.1007/978-0-387-30440-3

[29] R. Hirota and J. Satsuma, Soliton solutions of a coupled Korteweg-de Vries equation, Physics Letters A 85(8-9) (1981), 407-408.

DOI: https://doi.org/10.1016/0375-9601(81)90423-0

[30] H. Holden, B. Oksendal, J. Uboe and T. Zhang, Stochastic Partial Differential Equations, Birhkäuser: Basel, 1996.

[31] G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Computers & Mathematics with Applications 51(9-10) (2006), 1367-1376.

DOI: https://doi.org/10.1016/j.camwa.2006.02.001

[32] R. Khalil, M. Al Horani, A. Yousef and M Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics 264 (2014), 65-70.

DOI: https://doi.org/10.1016/j.cam.2014.01.002

[33] D. Kumar, A. R. Seadawy and A. K. Joardar, Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chinese Journal of Physics 56(1) (2018), 75-85.

DOI:https://doi.org/10.1016/j.cjph.2017.11.020

[34] Z. B. Li and H. J. He, Fractional complex transform for fractional differential equations, Mathematical and Computational Applications 15(5) (2010), 970-973.

DOI: https://doi.org/10.3390/mca15050970

[35] B. A. Li and M. L. Wang, Applications of F-expansion method to the coupled KdV system, Chinese Physics B 14(9) (2005), 1698-1706.

DOI: https://doi.org/10.1088/1009-1963/14/9/003

[36] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons: New York, 1993.

[37] Z. Odibat and S. Momani, Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order, Chaos, Solitons & Fractals 36(1) (2008), 167-174.

DOI: https://doi.org/10.1016/j.chaos.2006.06.041

[38] K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press: New York, 1974.

[39] I. Podlubny, Fractional Differential Equations, Academic Press: New York, 1999.

[40] M. Shateri and D. D. Ganji, Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique, International Journal of Differential Equations 2010(Sl1) (2010), 1-11.

DOI: https://doi.org/10.1155/2010/954674

[41] N. H. Sweilam, M. M. Khader and R. F. Al-Bar, Numerical studies for a multi-order fractional differential equation, Physics Letters A 371(1-2) (2007), 26-33.

DOI: https://doi.org/10.1016/j.physleta.2007.06.016

[42] M. Wadati, Stochastic Korteweg-de Vries equation, Journal of the Physical Society of Japan 52(8) (1983), 2642-2648.

DOI: https://doi.org/10.1143/JPSJ.52.2642

[43] M. L. Wang and Y. B. Zhou, The periodic wave solutions for the Klein–Gordon–Schrödinger equations, Physics Letters A 318(1-2) (2003), 84-92.

DOI: https://doi.org/10.1016/j.physleta.2003.07.026

[44] Y. M. Wang, M. L. Wang and J. L. Zhang, The periodic wave solutions for two systems of nonlinear wave equations, Chinese Physics B 12(12) (2003), 1341-1348.

DOI: https://doi.org/10.1088/1009-1963/12/12/001

[45] Y. M. Wang, M. L. Wang, J. L. Zhang, D. F. Ren and Z. D. Fang, The periodic wave solutions for the generalized Nizhnik?Novikov

[46] Y. T. Wu, X. G. Geng, X. B. Hu and S. M. Zhu, A generalized Hirota–Satsuma coupled Korteweg–de Vries equation and Miura transformations, Physics Letters A 255(4-6) (1999), 259-264.

DOI: https://doi.org/10.1016/S0375-9601(99)00163-2

[47] H. Yépez-Martínez and J. F. Gómez-Aguilar, Optical solitons solution of resonance nonlinear Schrödinger type equation with Atangana’s-conformable derivative using sub-equation method, Waves in Random and Complex Media 31(3) (2021), 573-596.

DOI: https://doi.org/10.1080/17455030.2019.1603413

[48] H. Yépez-Martínez, J. F. Gómez-Aguilar and A. Atangana, First integral method for non-linear differential equations with conformable derivative, Mathematical Modelling of Natural Phenomena 13(1) (2018); Article 14.

DOI: https://doi.org/10.1051/mmnp/2018012

[49] H. Yépez-Martínez, J. F. Gómez-Aguilar and D. Baleanu, Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion, Optik 155 (2018), 357-365.

DOI: https://doi.org/10.1016/j.ijleo.2017.10.104

[50] H. Yépez-Martínez and J. F. Gómez-Aguilar, Fractional sub-equation method for Hirota–Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivative, Waves in Random and Complex Media 29(4) (2019), 678-693.

DOI: https://doi.org/10.1080/17455030.2018.1464233

[51] S. Zhang, Q. A. Zong, D. Liu and Q. Gao, A generalized exp-function method for fractional Riccati differential equations, Communications in Fractional Calculus 1 (2010), 48-52.

[52] Y. B. Zhou, M. L. Wang and Y. M. Wang, Periodic wave solutions to a coupled KdV equations with variable coefficients, Physics Letters A 308(1) (2003), 31-36.

DOI: https://doi.org/10.1016/S0375-9601(02)01775-9