Solitary wave solutions and traveling wave solutions for systems of time-fractional nonlinear wave equations via an anal
- PDF / 2,255,176 Bytes
- 19 Pages / 439.37 x 666.142 pts Page_size
- 40 Downloads / 224 Views
Solitary wave solutions and traveling wave solutions for systems of time-fractional nonlinear wave equations via an analytical approach Hayman Thabet1 · Subhash Kendre1 · James Peters2,3 · Melike Kaplan4 Received: 4 December 2019 / Revised: 27 February 2020 / Accepted: 9 April 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract This paper introduces a new approximate-analytical approach for solving systems of Fractional Nonlinear Partial Differential Equations (FNPDEs). However, the main advantage of this new approximate-analytical approach is to obtain the analytical solution for general systems of FNPDEs in forms of convergent series with easily computable components using Caputo fractional partial derivative. Moreover, the convergence theorem and error analysis of the proposed method are also shown. Solitary wave solutions and traveling wave solutions for the system of fractional dispersive wave equations and the system of fractional long water wave equations are successfully obtained. The numerical solutions are also obtained in forms of tables and graphs to confirm the accuracy and efficiency of the suggested method. Keywords New approximate-analytical approach · Systems of fractional nonlinear partial differential equations · Systems of time-fractional nonlinear wave equations · Solitary wave solutions · Traveling wave solutions Mathematics Subject Classification 93C10 · 35R11
Communicated by Agnieszka Malinowska.
B
Hayman Thabet [email protected] Subhash Kendre [email protected] James Peters [email protected] Melike Kaplan [email protected]
1
Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India
2
Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Canada
3
Department of Mathematics, Faculty of Arts and Science, Adiyaman University, 02040 Adiyaman, Turkey
4
Department of Mathematics, Kastamonu University, Kastamonu, Turkey 0123456789().: V,-vol
123
144
Page 2 of 19
H. Thabet et al.
1 Introduction Over the last decades, Fractional Partial Differential Equations (FPDEs) have been a useful tool due to their wide uses for describing the natural phenomena of science and engineering models where the nonlinear wave theory frequently explores asymptotic regimes (such as varying over many scales, high frequency or large amplitude) which are not easily accessible via numerical simulations (see, e.g., Dehghan and Abbaszadeh 2016; Mohebbi Ghandehari and Ranjbar 2013; Thabet and Kendre 2018a, b; Thabet et al 2019b). Solitary waves were discovered by the naval architect John Scott Russell in 1834. When a canal barge hit an underwater obstruction and stopped suddenly, Russell expected that the bow wave would dissolve into lots of little ripples through dispersion. Instead, a smooth, bell-shaped crest perhaps half a meter tall, independent of the cross-channel direction, emerged from the froth. The system of FNPDEs have been increasingly used to represent physical and control systems (see,
Data Loading...
