Different soliton solutions to the modified equal-width wave equation with Beta-time fractional derivative via two different methods

Abstract

‎In this paper‎, ‎different types of soliton solutions of the modified equal width wave (MEW) equation with beta time derivative are obtained by implementing the two different methods named as‎: ‎extended Jacobi's elliptic expansion function method and Kudryashov method‎. ‎The dark‎, ‎bright‎, ‎singular and other solitons are achieved‎. ‎The obtained soliton solutions are verified through MATHEMATICA‎. ‎At the end‎, ‎the results are also explained through graphs‎. ‎These soliton solutions suggest that these two methods are effective‎, ‎straight forward and reliable as compare to other methods‎. ‎The obtained results can be used in describing the substantial understanding of the studious structures as well as others related non-linear physical structures‎.

New analytical wave solutions to the M-fractional Kuralay-II equations based on three distinct schemes

“…Fractional partial differential equations (FPDEs) play an important role in many areas of sciences instantly; biology, applied physics, chemistry, economics etc. Naturally occurring phenomenon can be represent in the form of non-linear PDEs i.e Extended Zakharov-Kuzetsov equation [1], Modified equal-width wave equation [2], Pertubed Gerdjikov-Ivanov equation [3], Biswas-Arshed equation [4], Schrödinger-Hirota equation [5], Biological population equation [6], Diffusion-reaction equation [7], Chen-Lee-Liu equation [8], Radhakrishnan-Kundu-Lakshmanan equation [9], Heisenberg ferromagnetic spin chain equation [11], higher-dimensional telegraph equation [12], generalized Burgers-Huxley equation [13] etc. There are many different schemes that are used to find the distinct types of exact solitons i.e Jacobi elliptic function technique [14], Hirota bilinear method [15], Kudryashov method [16], Modified extended tanh expansion method [17] etc.…”

Exploring the Analytical Solutions to the Economical Model via Three Different Methods

“…Many mathematical models have been developed in many areas of sciences in the form of nonlinear partial diferential equations (NLPDEs). Numerous techniques are made to gain exact solutions of NLPDEs such as generalized exponential rational function scheme (GERFS) [1][2][3][4], (m + 1/G)-expansion and Adomian decomposition schemes [5], new generalized expansion method [6], simplest equation and Kudryashov's new function techniques [7], modifed simple equation scheme [8], modifed Kudryashov simple equation technique [9], frst integral technique [10], Bäcklund transformation scheme [11], extended jacobi elliptic function expansion technique [12], and extended (G/G)-expansion and improved (G ′ /G)-expansion schemes [13].…”

Investigation of Exact Solutions of M-fractional Ivancevic Option Pricing Model Based on Three Different Methods

“…Liu's extended trial function method (LETFM) [4], generalized unified method (GUM) [5], sine-Gordon expansion technique (SGET) [6], enhanced modified simple equation scheme [7],unified technique [8], extended tanh function scheme [9], Lie symmetry technique [10], symbolic computational method, Hirota's simple method and long wave technique [11], Jacobi elliptic function expansion scheme [12], Elzaki transform decomposition technique [13], (m + 1 G )-expansion and adomian decomposition schemes [14], new generalized expansion method [15], simplest equation and kudryashov's new function techniques [16], modified simple equation scheme [17], modified kudryashov simple equation technique [18], first integral technique [19], Bäcklund transformation scheme [20], extended jacobi elliptic function expansion technique [21], extended (G/G)-expansion and improved (G ′ /G)-expansion schemes [30] etc. There are three other methods; exp a function, extended Sinh-Gordon equation expansion (EShGEE) and extended (G ′ /G)-expansion methods.…”