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Exact Soliton Solutions of the Space-Time Fractional Kadomtsev–Petviashvili Equation via the Tanh–Coth Method under the Conformable Fractional Derivative
Research Article - Volume: 1, Issue: 1, 2026 (October)
Exact Soliton Solutions of the Space-Time Fractional Kadomtsev–Petviashvili Equation via the Tanh–Coth Method under the Conformable Fractional Derivative Download PDF

Najib Bello Halilu1*, Abubakar Suleman Muhammad1, Kabiru Isah1, Karuna Laddha1, Pramod Mehta1, Komal Prajapat1, Aminu Salisu Taambu1, Isah Tasiu Basiru1, Habibu Muhammad Haris1, Adamu Musa Garba1

1Department of Mathematics, Faculty of Science and Technology, Mewar University, Gangrar, Chittorgarh, Rajasthan, India

*Correspondence to: Najib Bello Halilu, Department of Mathematics, Faculty of Science and Technology, Mewar University, Gangrar, Chittorgarh, Rajasthan, India, E-mail:

Received: August 18, 2026; Manuscript No: JMPM-26-7846; Editor Assigned: August 20, 2026; PreQc No: JMPM-26-7846 (PQ); Reviewed: August 26, 2026; Revised: August 31, 2026; Manuscript No: JMPM-26-7846 (R); Published: October 01, 2026

ABSTRACT

The study derives exact travelling-wave solutions of the space–time fractional Kadomtsev– Petviashvili equation using the tanh–coth method with conformable fractional derivatives. The method reduces the fractional PDE to a nonlinear ODE and produces eight solution branches, including hyperbolic, trigonometric, singular, dark, and rational structures. The solutions are verified symbolically, while the fractional order is shown to influence wave amplitude, width, localization, and propagation characteristics. Wolfram Mathematica software is used for plotting 3D, 2D and contour plots. .

Keywords: Conformable Fractional Derivative; Space–Time Fractional Kadomtsev–Petviashvili Equation; Tanh–Coth Method; Exact Soliton Solutions; Nonlinear Evolution Equations

Citation: Halilu NB, Abubakar SM, Isah K, Laddha K, Mehta P, Prajapat K, et al. (2026). Exact Soliton Solutions of the Space-Time Fractional Kadomtsev–Petviashvili Equation via the Tanh–Coth Method under the Conformable Fractional Derivative. J. Math. Phys. Mech. Vol.1 Iss.1, October (2026), pp:116-132.
Copyright: © 2026 Najib Bello Halilu, Abubakar Sulaiman Muhammad, Kabiru Isah, Karuna Laddha, Pramod Mehta, Komal Prajapat, Aminu Salisu Taambu, Isah Tasiu Basiru, Habibu Muhammad Haris, Adamu Musa Garba. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.