[1] Abdeljawad, T. On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015),
57–66. https://doi.org/10.1016/j.cam.2014.10.016
[2] Albalawi, W., Shah, R., Shah, N.A., Chung, J.D., Ismaeel, S.M. and El-Tantawy, S.A.
Analyzing both fractional porous media and heat transfer equations via some novel techniques,
Mathematics 11 (2023), 1350. https://doi.org/10.3390/math11061350
[3] Angstmann, C.N. and Henry, B.I. Time fractional Fisher–KPP and FitzHugh–Nagumo
equations, Entropy 22(9) (2020), 1035. https://doi.org/10.3390/e22091035
[4] Apostol, T.M. Calculus, Vol. 1, 2nd ed., Blaisdell Publishing Company, Waltham, MA,
1967.
[5] Arqub, O.A., Edwan, R., Al-Smadi, M. and Momani, S. Solving space-fractional Cauchy
problem by modified finite-difference discretization scheme, Alexandria Eng. J. 59 (2020),
2409–2417. https://doi.org/10.1016/j.aej.2020.01.041
[6] Aychluh, M. and Ayalew, M. The fractional power series method for solving the non-
linear Kuramoto–Sivashinsky equation, Int. J. Appl. Comput. Math. 11 (2025), 29.
https://doi.org/10.1007/s40819-025-01850-9
[7] Atangana, A. A note on the triple Laplace transform and its applications to some kind of
third-order differential equation, Abstr. Appl. Anal. 2013 (2013), Article ID 769102, 1–10.
https://doi.org/10.1155/2013/769102
[8] Berkovich, L.M. Factorization as a method of finding exact invariant solutions of the
Kolmogorov–Petrovskii–Piskunov equation and the related Semenov and Zeldovich equations,
Sov. Math. Dokl. 45 (1992), 162–167.
[9] Boulaaras, S., Jan, R. and Pham, V.T. Recent advancement of fractional calculus and
its applications in physical systems, Eur. Phys. J. Spec. Top. 232 (2023), 2347–2350.
https://doi.org/10.1140/epjs/s11734-023-01002-4
[10] Cabré, X., Coulon, A.C. and Roquejoffre, J.-M. Propagation in Fisher–KPP type equa-
tions with fractional diffusion in periodic media, C. R. Math. 350(19–20) (2012), 885–890.
https://doi.org/10.1016/j.crma.2012.10.007
[11] Cabré, X. and Roquejoffre, J.-M. Front propagation in Fisher–KPP equations with fractional
diffusion, C. R. Acad. Sci. Paris Ser. I 347 (2009), 1361–1366.
[12] Cabré, X. and Roquejoffre, J.-M. The influence of fractional diffusion in Fisher–KPP equa-
tions, Commun. Math. Phys., submitted for publication, 2012.
[13] Chellaboina, V., Bhat, S.P., Haddad, W.M. and Bernstein, D.S. Modeling and analysis of
mass-action kinetics, IEEE Control Syst. Mag. 29 (2009), 60–78.
[14] Cui, R. and Hu, Y. Fractional power series method for solving fractional differential equation,
J. Adv. Math. 14(4) (2016), 6156–6159.
[15] Duan, J.S., Rach, R., Baleanu, D. and Wazwaz, A.M. A review of the Adomian decomposi-
tion method and its applications to fractional differential equations, Commun. Fract. Calc.
3 (2012), 73–99.
[16] El-Ajou, A., Arqub, O.A., Zhour, Z.A. and Momani, S. New results on
fractional power series: theories and applications, Entropy 15 (2013), 5305–
5323.https://doi.org/10.3390/e15125305
[17] Eroğlu, B.İ., Avci, D. and Özdemir, N. Optimal control problem for a con-
formable heat conduction equation, Acta Phys. Pol. A 132 (2017), 658–662.
https://doi.org/10.12693/APhysPolA.132.658
[18] Fasano, A., Herrero, M.A. and Rodrigo, M.R. Slow and fast invasion waves
in a model of acid-mediated tumour growth, Math. Biosci. 220 (2009), 45–56.
https://doi.org/10.1016/j.mbs.2009.05.003
[19] Fisher, R.A. The wave of advance of advantageous genes, Ann. Eugen. 7 (1937), 353–369.
[20] Fuentes, M.A., Kuperman, M.N. and Kenkre, V.M. Nonlocal interaction effects on pattern
formation in population dynamics, Phys. Rev. Lett. 91 (2003), 158104.
[21] Giusti, A., Colombaro, I., Garra, R., Garrappa, R. and Mentrelli, A. On variable-
order fractional linear viscoelasticity, Fract. Calc. Appl. Anal. 27 (2024), 1564–1578.
https://doi.org/10.1007/s13540-024-00288-y
[22] Griffiths, G. and Schiesser, W.E. Traveling Wave Analysis of Partial Differential Equations:
Numerical and Analytical Methods with MATLAB and Maple, Academic Press, Amsterdam,
2010. https://doi.org/10.1016/B978-0-12-384652-5.00010-8
[23] Habenom, H., Suthar, D.L. and Mulualem, A. Solution of fractional Fokker–Planck equation
using fractional power series method, J. Sci. Arts 3(48) (2019), 593–600.
[24] Hamel, F. and Roques, L. Fast propagation for KPP equations with slowly
decaying initial conditions, J. Differential Equations 249 (2010), 1726–1745.
https://doi.org/10.1016/j.jde.2010.06.005
[25] Hariharan, G. The homotopy analysis method applied to the Kolmogorov–Petrovskii–
Piskunov (KPP) and fractional KPP equations, J. Math. Chem. 51 (2013), 992–1000.
https://doi.org/10.1007/s10910-012-0132-5
[26] Jarad, F., Uğurlu, E., Abdeljawad, T. and Baleanu, D. On a new class of fractional opera-
tors, Adv. Difference Equ. 2017(1) (2017), 247. https://doi.org/10.1186/s13662-017-1306-z
[27] Khaled, A.G. The homotopy perturbation method applied to the nonlinear fractional
Kolmogorov–Petrovskii–Piskunov equations, Appl. Math. Lett. 24 (2011), 1428–1434.
https://doi.org/10.1016/j.aml.2011.03.025
[28] Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M. A new definition of fractional deriva-
tive, J. Comput. Appl. Math. 264 (2014), 65–70. https://doi.org/10.1016/j.cam.2014.01.002
[29] Khan, S.Y. and Ahmed, S.A. An approximate solution of fractional Kolmogorov–
Petrovskii–Piskunov equations, MATEMATIKA 35(3) (2019), 377–385.
https://doi.org/10.11113/matematika.v35.n3.1170
[30] Khan, Y. and Wu, Q. Homotopy perturbation transform method for nonlinear
equations using He’s polynomials, Comput. Math. Appl. 61 (2011), 1963–1967.
https://doi.org/10.1016/j.camwa.2010.08.016
[31] Kolmogorov, A.N., Petrovskii, I. and Piskunov, N. A study of the diffusion equation
with increase in the amount of substance and its application to a biology problem, Byul.
Moskovskogo Gos. Univ. 1 (1937), 1–25.
[32] Murray, J.D. Mathematical Biology I: An Introduction, 3rd ed., Springer, New York, 2001.
[33] Özkan, O. and Kurt, A. The analytical solutions for conformable integral equations and
integro-differential equations by conformable Laplace transform, Opt. Quantum Electron.
50 (2018), 81. https://doi.org/10.1007/s11082-018-1342-2
[34] Ross, B. Fractional Calculus and Its Applications, Proceedings of the International Confer-
ence Held at the University of New Haven, June 1974, Springer-Verlag, Berlin, 1975.
[35] Silva, F.S., Moreira, D.M. and Moret, M.A. Conformable Laplace transform of fractional
differential equations, Axioms 7 (2018), 55. https://doi.org/10.3390/axioms7030055
[36] Thabet, H., Kendre, S. and Peters, J. Analytical solutions for nonlinear systems of con-
formable space-time fractional partial differential equations via generalized fractional dif-
ferential transform, Vietnam J. Math. 47 (2019), 487–507. https://doi.org/10.1007/s10013-
019-00340-y
[37] Unal, A.O. On the Kolmogorov-Petrovskii-Piskunov equation, Commun. Fac. Sci. Univ. Ank.
Ser. A1 Math. Stat. 62 (2013), 1–10.
[38] Wu, G.C. New trends in the variational iteration method, Commun. Fract. Calc. 2 (2011),
59–75.
[39] Zhao, D. and Luo, M. General conformable derivative and its physical interpretation, Calcolo
54 (2017), 903–917. https://doi.org/10.1007/s10092-017-0213-8
