New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations
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Akman T, Yildiz B, Baleanu D (2017) New discretization of caputofabrizio derivative. Comput Appl Math. https://doi.org/10.1007/s40314-017-0514-1
Albuohimad B, Adibi H, Kazem S (2017) A numerical solution of time-fractional coupled korteweg-de vries equation by using spectral collection method. Ain Shams Engineering Journal (In Press)
Algahtani OJJ (2016) Comparing the atangana-baleanu and caputo-fabrizio derivative with fractional order: Allen cahn model. Chaos, Solitons Fractals 89:552–559
Atangana A (2016) On the new fractional derivative and application to nonlinear fishers reaction diffusion equation. App Math Comput 273:948–956
Atangana A, Badr STA (2015) Analysis of the keller-segel model with a fractional derivative without singular kernel. Entropy 17:4439–4453
Atangana A, Nieto JJ (2015) Numerical solution for the model of rlc circuit via the fractional derivative without singular kernel. Adv Mech Eng 7:1–7
Atangana A, Badr STA (2016) New model of groundwater flowing within a confine aquifer: Application of caputo-fabrizio derivative. Arabian Journal of Geosciences, 2060–8. https://doi.org/10.1007/s12517-015
Atangana A, Secer A (2013) The time-fractional coupled-korteweg-de-vries equations, Abstract and Applied Analysis 2013, Article ID 947986, 8 pages
Badr STA, Atangana A (2015) Extension of the rlc electrical circuit to fractional derivative without singular kernel. Adv Mech Eng 7(6):1–6
Baleanu D, Atangana A (2016) New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm Sci 20:763–769
Bhrawy AH, Doha EH, Ezz-Eldien SS, Abdelkawy MA (2015) A numerical techniqe based on the shifted legendre polynomials for solving the time fractional coupled kdv equations. Calcolo 53:1–17
Cao W, Xu Y, Zheng Z (2018) Finite difference/collocation method for a generalized time-fractional KDV equation. Appl Sci 8(1):42
Caputo M, Fabrizio M (2015) A new definition of fractional derivative without singular kernel. Progr Fract Differ Appl 2:1–13
Caputo M, Fabrizio M (2016) Applications of new time and spatial fractional derivatives with exponential kernels. Progr Fract Differ Appl 2:1–11
El-Ajou A, Abu Arqub O, Momani S (2015) The time-fractional coupled-korteweg-de-vries equations. J Comput Phys 293:81–95
El-Tawil MA, Huseen SN (2012) The q-homotopy analysis method (q-ham). Int J Appl Math Mech 8:51–75
El-Tawil MA, Huseen SN (2013) On convergence of the q-homotopy analysis method. Int J Contemp Math Sci 8(10):481–497
Etemad S, Rezapour S, Alsaedi A, Baleanu D (2016) On coupled systems of time-fractional differential problems by using a new fractional derivative. J Fun Spaces 2016:1–16
Feng Z (2003) Travelling wave solutions and proper solutions to the two-dimensional Burgerskortewegde Vries equation. J Phys A (Math Gen) 36:8817–8827
Feng Z (2007) On travelling wave solutions of the burgerskortewegde vries equation. Nonlinearity 20:343–356
Gao F, Yang XJ, Mohyud-Din ST (2017) On linear viscoelasticity within general fractional derivatives without singular kernel. Thermal Sci 21:S335–S342
Gómez-Aguilar JF (2017) Irving-Mullineux oscillator via fractional derivatives with Mittag-Leffler kernel. Chaos, Solitons Fractals 95:179–186
Guo Y (2017) Exponential stability analysis of travelling waves solutions for nonlinear delayed cellular neural networks. Dyn Syst 32:490–503
Johnson RS (1970) A non-linear equation incorporating damping and dispersion. J Fluid Mech 42(1):49–60
Kath WL, Smyth NF (1995) Soliton evolution and radiation loss for the Korteweg-de Vries equation. Phys Rev E 51(3):661–670
Khan A, Ali Abro K, Tassaddiq A, Khan I (2017) Atangana-baleanu and caputo-fabrizio analysis of fractional derivatives for heat and mass transfer of second grade fluids over a vertical plate: a comparative study. Entropy 19(8):1–12
Koca I (2017) Analysis of rubella disease model with non-local and non-singular fractional derivatives. Int J Optim Control: Theories Appl (IJOCTA) 8(1):17–25
Koca I, Atangana A (2016) Chaos in a simple nonlinear system with atangana? Baleanu derivatives with fractional order. Chaos, Solitons Fractals 1:1–18
Koca I, Atangana A (2016) Solutions of cattaneo-hristov model of elastic heat diffusion with Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. Thermal Sci 1:103–113
Korteweg DJ, de Vries G (1895) On the change of form of long waves advancing in a rectangular channel, and on a new type of long stationary waves. Phil Mag 39:422–443
Liao SJ (1992) The proposed homotopy analysis technique for the solution of nonlinear problems, PhD thesis, Shanghai Jiao Tong University
Liao SJ (2003) Beyond perturbation: introduction to the homotopy analysis method. Chapman and Hall/CRC Press, Boca Raton
Liao SJ (2005) Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput 169:1186–1194
Mainardi F, Caputo M (1971) A new dissipation model based on memory mechanism. Pure Appl Geophys 91:134–147
Manjarekar S, Bhadane AP (2017) Generalized elzaki-tarig transformation and its applications to new fractional derivative with non singular kernel. Progr Fract Differ Appl 3(3):227–232
Nieto JJ, Losada J (2015) Properties of a new fractional derivative without singular kernel. Progr Fract Differ Appl 2:87–92
Owolabi KM, Atangana A (2017) Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reactiondiffusion systems. Comp Appl Math. https://doi.org/10.1007/s40314-017-0445-x
Podlubny I (1999) Fractional differential equations. Academic Press, San Diego
Saad KM (2018) Comparing the caputo, caputo-fabrizio and atangana-baleanu derivative with fractional order: fractional cubic isothermal auto-catalytic chemical system. The European Physical Journal Plus 133:94
Sahoo S, Ray S Saha (2017) A new method for exact solutions of variant types of time-fractional Korteweg-de Vries equations in shallow water waves. Math Methods Appl Sci 40(1):106–114
Singh J, Kumar D, Baleanu D (2017) On the analysis of chemical kinetics system pertaining to a fractional derivative with mittag-leffler type kernel. Chaos Interdiscip J Nonlinear Sci 27(10):103–113
Singha J, Kumara D, Baleanub D (2017) A new analysis for fractionalmodel of regularized long-wave equation arising in ion acoustic plasma waves. Math Methods Appl Sci 40:5642–5653
Yang XJ, Gao F, Srivastava HM (2017) A new computational approach for solving nonlinear local fractional PDEs. Journal of Computational and Applied Mathematics (In Press)
Yang XJ (2017) Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems. Thermal Sci 21(3):1161–1171
Yang XJ (2017) General fractional calculus operators containing the generalized Mittag-Leffler functions applied to anomalous relaxation. Thermal Sci 21:S317–S326
Yang XJ (2017) A new integral transform operator for solving the heat-diffusion problem. Appl Math Lett 64:193–197
Yang XJ (2018) New rheological problems involving general fractional derivatives with nonsingular power-law kernels. Proc Roman, Ser A 19(1):45–52
Yang XJ, Machado JAT (2017) A new fractional operator of variable order: application in the description of anomalous diffusion. Physica A: Stat Mech Appl 481:276–283
Yang XJ, Hristov J, Srivastava HM, Ahmad B (2014) Modelling fractal waves on shallow water surfaces via local fractional Korteweg-de Vries equation. Abstr Appl Anal 2014 278672:10
Yang XJ, Machado JA Tenreiro, Baleanu D, Cattani C (2016) A new method for exact solutions of variant types of time-fractional Korteweg-de Vries equations in shallow water waves. Chaos Interdiscip J Nonlinear Sci 26(8):084312
Yang XJ, Baleanu D, Gao F (2017) New analytical solutions for Klein-Gordon and Helmholtz equations in fractal dimensional space. Proc Roman Acad Ser A: Math Phys Tech Sci Inf Sci 18(3):231–238
Yang XJ, Machado JT, Baleanu D (2017) Anomalous diffusion models with general fractional derivatives within the kernels of the extended Mittag-Leffler type functions. Roman Rep Phys 69(4):115
Yang XJ, Srivastava HM, Torres DFM, Debbouche A (2017) General fractional-order anomalous diffusion with nonsingular power-law kernel. Thermal Sci 21(1):S1–S9