Solitary wave solutions of Fitzhugh–Nagumo-type equations with conformable derivatives

The Fitzhugh–Nagumo equation is an important non-linear reaction–diffusion equation used to model the transmission of nerve impulses. This equation is used in biology as population genetics; the Fitzhugh–Nagumo equation is also frequently used in circuit theory. In this study, we give solutions to the fractional Fitzhugh–Nagumo (FN) equation, the fractional Newell–Whitehead–Segel (NWS) equation, and the fractional Zeldovich equation. We found the exact solutions of these equations by conformable derivatives. We have obtained the exact solutions within the time-fractional conformable derivative for these equations.

[1]  A. Cevikel.  Traveling wave solutions of conformable Duffing model in shallow water waves , 2022, International Journal of Modern Physics B.

[2]  A. Cevikel.  New solutions for the high-dimensional fractional BLMP equations , 2022, Journal of Ocean Engineering and Science.

[3]  Adem C. Cevikel,et al.  New impressive representations for the soliton behaviors arising from the (2+1)-Boussinesq equation , 2022, Journal of Ocean Engineering and Science.

[4]  S. Momani,et al.  On group of Lie symmetry analysis, explicit series solutions and conservation laws for the time-fractional (2 + 1)-dimensional Zakharov-Kuznetsov (q,p,r) equation , 2022, Journal of Geometry and Physics.

[5]  A. Yusuf,et al.  Fractional dynamics and analysis for a lana fever infectious ailment with Caputo operator , 2021, Chaos, Solitons & Fractals.

[6]  D. Baleanu,et al.  A new and general fractional Lagrangian approach: A capacitor microphone case study , 2021, Results in Physics.

[7]  J. Nieto,et al.  A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects , 2021, Alexandria Engineering Journal.

[8]  V. S. Erturk,et al.  Novel Fractional-Order Lagrangian to Describe Motion of Beam on Nanowire , 2021, Acta Physica Polonica A.

[9]  Adem Cengiz Çevikel,et al.  Soliton solutions of nonlinear fractional differential equations with its applications in mathematical physics , 2021 .

[10]  H. Rezazadeh,et al.  Exact optical solitons to the perturbed nonlinear Schrödinger equation with dual-power law of nonlinearity , 2020, Optical and Quantum Electronics.

[11]  H. Rezazadeh,et al.  The Functional Variable Method to Find New Exact Solutions of the Nonlinear Evolution Equations with Dual-Power-Law Nonlinearity , 2020 .

[12]  Adem C. Cevikel,et al.  Study on Fractional Differential Equations with Modified Riemann–Liouville Derivative via Kudryashov Method , 2019, International Journal of Nonlinear Sciences and Numerical Simulation.

[13]  Ahmet Bekir,et al.  The exp-function method for some time-fractional differential equations , 2017, IEEE/CAA Journal of Automatica Sinica.

[14]  Adem C. Cevikel,et al.  Soliton solutions of (2+1)-dimensional time-fractional Zoomeron equation , 2016 .

[15]  Hadi Rezazadeh,et al.  The first integral method for Wu–Zhang system with conformable time-fractional derivative , 2016 .

[16]  Adem C. Cevikel,et al.  Exact Solutions for Fractional Differential-Difference Equations by (G'/G)-Expansion Method with Modified Riemann-Liouville Derivative , 2016 .

[17]  Adem C. Cevikel,et al.  Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method , 2015 .

[18]  Thabet Abdeljawad,et al.  On conformable fractional calculus , 2015, J. Comput. Appl. Math..

[19]  M. Sababheh,et al.  A new definition of fractional derivative , 2014, J. Comput. Appl. Math..

[20]  N. Taghizadeh,et al.  Application of the simplest equation method to some time-fractional partial differential equations , 2013 .

[21]  A. Bekir,et al.  New Solitons and Periodic Solutions for (2+1)-dimensional Davey-Stewartson Equations , 2013 .

[22]  Adem C. Cevikel,et al.  A procedure to construct exact solutions of nonlinear evolution equations , 2012 .

[23]  Adem C. Cevikel,et al.  Solitary wave solutions of two nonlinear physical models by tanh–coth method , 2009 .

[24]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[25]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[26]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[27]  Adem C. Cevikel,et al.  New exact solutions of the space-time fractional KDV burgers and nonlinear fractional foam drainage equation , 2017 .

[28]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .