Title: Soliton solutions of space-time fractional Zoomeron differential equation

Authors: Hamood Ur Rehman; Muhammad Imran Asjad; Ifrah Iqbal; Ali Akgül

Addresses: Department of Mathematics, University of Okara, Okara, Pakistan ' Department of Mathematics, University of Management and Technology, Lahore, Pakistan ' Department of Mathematics, University of Okara, Okara, Pakistan ' Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey; Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, 99138, Nicosia/Mersin 10, Turkey

Abstract: In the present work, Sardar subequation method (SSM) is exerted for seeking exact solutions of (2 + 1)-dimensional space-time fractional Zoomeron equation (FZE) in terms of conformable derivative (CD). The conformable derivative has much more capability than Riemann-Liouville and caputo derivative in solving the nonlinear fractional differential equation. The proposed method is extremely simple and very effective for finding exact solutions and then extracting solitons for the model. Bright, dark, singular, periodic singular and bright-dark hybrid soliton solutions are retrieved. Appropriate constraints are chosen for the obtained solitons to guarantee their existence. Moreover, from some obtained solutions, we draw its two-dimensional, contour and three-dimensional graphs by taking suitable values of parameters and then compare these graphs by changing the values of conformable derivative.

Keywords: space-time fractional Zoomeron equation; FZE; Sardar subequation method; SSM; conformable derivative; CD; nonlinear partial fractional differential equations; NLFPDEs.

DOI: 10.1504/IJANS.2023.133734

International Journal of Applied Nonlinear Science, 2023 Vol.4 No.1, pp.29 - 46

Received: 02 Aug 2022
Accepted: 14 Nov 2022

Published online: 02 Oct 2023 *

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