Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
13th International Engine Congress 2026 | 24 + 25 February 2026

Meeting Place for the Powertrain and Sustainable Fuels Community

Take part as a speaker in the 13th International Engine Congress 2026, the Meeting Place for the Powertrain, and Sustainable Fuels Community for the exchange of experience. Submit a subject proposal online about our main subject areas: Passenger car engine technology, Commercial vehicle engine technology and Sustainable Fuels & Energy!
EXTENDED SEARCH
Log in
Top
Published in:
Read chapter Read first chapter

2024 | OriginalPaper | Chapter

Approximate Solutions of the Fractional Zakharov-Kuznetsov Equation Using Laplace-Residual Power Series Method

Authors : Tareq Eriqat, Moa’ath N. Oqielat, Ahmad El-Ajou, Osama Ogilat, Shaher Momani

Published in: Mathematical Analysis and Numerical Methods

Publisher: Springer Nature Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

An analytical solution is proposed in this work for the non-linear time-fractional Zakharov-Kuznetsov partial differential equation (FZK-PDE) in the Caputo sense. The FZK-PDE model demonstrates the behavior of weakly nonlinear ion-acoustic waves in a plasma with a uniform magnetic field. A series solution for the FZK-PDE is obtained using the so-called Laplace-Residual power series method (L-RPSM). The L-RPSM is a simple and efficient technique for obtaining approximate and exact series solution of nonlinear and linear fractional differential equations (FDEs). Graphical and numerical solutions of several test examples show the reliability and efficiency of the L-RPSM. Moreover, the results show that the L-RPSM is powerful, competitive, simple, and reliable for a wide range of fractional PDEs.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Stochastic Population Growth Model Using Three-Point Fractional Formula
next chapter Reducing Data Sparsity in Movie Recommendation System
Literature
1.
Kilbasi, A., Saigo, M.: On Mittag-Leffler type function, fractional Calculas operators and solutions of integral equations. Integr. Trans. Spec. Funct. 4(4), 355–370 (1996)CrossRef
2.
Almeida, R., Tavares, D., Torres, D.: The Variable-Order Fractional Calculus of Variations. Springer (2019)
3.
Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley (1993)
4.
Oldham, K., Spanier, J.: The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order. Elsevier (1974)
5.
Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications. Elsevier (1998)
6.
Mainardi, F.: Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. World Scientific (2010)
7.
Kazem, S.: Exact solution of some linear fractional differential equations by Laplace transform. Int. J. Nonlinear Sci. 16(1), 3–11 (2013)MathSciNet
8.
Momani, S.: Non-perturbative analytical solutions of the space-and time-fractional Burgers equations. Chaos, Solit. Fractals 28(4), 930–937 (2006)
9.
Das, S.: Analytical solution of a fractional diffusion equation by variational iteration method. Comput. Math. Appl. 57(3), 483–487 (2009)MathSciNetCrossRef
10.
Momani, S., Odibat, Z.: Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations. Comput. Math. Appl. 54(7–8), 910–919 (2007)MathSciNetCrossRef
11.
El-Ajou, A., Abu Arqub, O., Momani, S.: Solving fractional two-point boundary value problems using continuous analytic method. Ain Shams Eng. J. 4(3), 539–547 (2013)
12.
Shqair, M., El-Ajou, A., Nairat, M.: Analytical solution for multi-energy groups of neutron diffusion equations by a residual power series method. Mathematics 7(7), 633 (2019)CrossRef
13.
El-Ajou, A., Al-Zhour, Z., Momani, S., Hayat, T.: Series solutions of nonlinear conformable fractional KdV-Burgers equation with some applications. Eur. Phys. J. Plus 134(8), 402 (2019)CrossRef
14.
Oqielat, M., El-Ajou, A., Al-Zhour, Z., Alkhasawneh, R., Alrabaiah, H.: Series solutions for nonlinear time-fractional Schrödinger equations: comparisons between conformable and caputo derivatives. Alex. Eng. J. (2020)
15.
Eriqat, T., El-Ajou, A., Oqielat, M., Al-Zhour, Z., Momani, S.: A new attractive analytic approach for solutions of linear and nonlinear neutral fractional pantograph equations. Chaos, Solit. Fractals 138, 109957 (2020)
16.
El-Ajou, A.: Adapting the Laplace transform to create solitary solutions for the nonlinear time-fractional dispersive PDEs via a new approach. Eur. Phys. J. Plus 136(2), 1–22 (2021)CrossRef
17.
Eriqat, T., Oqielat, M., Al-Zhour, Z., El-Ajou, A., Bataineh, A.: Revisited fisher’s equation and logistic system model: a new fractional approach and some modifications. Int. J. Dyn. Control 1–10 (2022)
18.
Oqielat, M., Eriqat, T., Al-Zhour, Z., Ogilat, M., El-Ajou, A., Hashim, I.: Construction of fractional series solutions to nonlinear fractional reaction–diffusion for bacteria growth model via Laplace residual power series method. Int. J. Dyn. Control 1–8 (2022)
19.
Oqielat, M., El-Ajou, A., Al-Zhour, Z., Eriqat, T., Al-Smadi, M.: A new approach to solving Fuzzy quadratic Riccati differential equations. Int. J. Fuzzy Log. Intell. Syst. 22, 23–47 (2022)CrossRef
20.
Oqielat, M., Eriqat, T., Ogilat, M., Odibat, Z., Al-Zhour, Z., Hashim, I.: Approximate solutions of fuzzy fractional population dynamics model. Eur. Phys. J. Plus 137(8), 1–16 (2022)CrossRef
21.
Oqielat, M., Eriqat, T., Al-Zhour, Z., El-Ajou, A., Momani, S.: Numerical solutions of time-fractional nonlinear water wave partial differential equation via Caputo fractional derivative: An effective analytical method and some applications. Appl. Comput. Math. 21(2), 207–222 (2022)MathSciNet
22.
Zakharov, V.E., Kuznetsov, E.A.: On threedimensional solitons. Zhurnal Eksp. Teoret. Fiz 66, 594–597 (1974)
23.
Munro, S., Parkes, E.J.: The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions. J. Plasma Phys. 62(3), 305–317 (1999)CrossRef
24.
Munro, S., Parkes, E.J.: Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation. J. Plasma Phys. 64(4), 411–426 (2000)CrossRef
25.
Molliq, R., Noorani, M., Hashim, I., Ahmad, R.R.: Approximate solutions of fractional Zakharov–Kuznetsov equations by VIM. J. Comput. Appl. Math. 233(2), 103–108 (2009)
26.
Yıldırım, A., Gülkanat, Y.: Analytical approach to fractional Zakharov-Kuznetsov equations by He’s homotopy perturbation method. Commun. Theor. Phys. 53(6), 1005 (2010)MathSciNetCrossRef
27.
Shah, R., Khan, H., Baleanu, D., Kumam, P., Arif, M.: A novel method for the analytical solution of fractional Zakharov-Kuznetsov equations. Adv. Differ. Equ. 2019(1), 1–14 (2019)MathSciNetCrossRef
28.
Şenol, M., Alquran, M., Kasmaei, H.: On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation. Results Phys. 9, 321–327 (2018)CrossRef
29.
El-Ajou, A.: Taylor’s expansion for fractional matrix functions: theory and applications. J. Math. Comp. Sci. 21(1), 1–17 (2020)CrossRef
Metadata
Title
Approximate Solutions of the Fractional Zakharov-Kuznetsov Equation Using Laplace-Residual Power Series Method
Authors
Tareq Eriqat
Moa’ath N. Oqielat
Ahmad El-Ajou
Osama Ogilat
Shaher Momani
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Mathematical Analysis and Numerical Methods

Print ISBN: 978-981-9748-75-4

Electronic ISBN: 978-981-9748-76-1

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-4876-1_32

Premium Partner

    Image Credits