| Citation: |
Shahid Ali, Ahmad Javid. EXPLICIT SOLUTIONS FOR THE CONFORMABLE REGULARIZED LONG WAVE BURGER'S EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 344-358. doi: 10.11948/20220135
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EXPLICIT SOLUTIONS FOR THE CONFORMABLE REGULARIZED LONG WAVE BURGER'S EQUATION
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Abstract
In this paper, a dynamical analysis of the conformable regularized long-wave burgers equation is carried out with help of improved $ \tan\big(\frac{\phi(\eta)}{2}\big) $-expansion method. Fractional complex transform converts a nonlinear fractional differential equation in an ordinary differential form which resulted into a number of exact solutions like exponential function solutions, hyperbolic function solutions, trigonometric function solutions and rational function solutions. The constarint conditions are also given for each solution. The physical profiles of proposed solutions are portrayed by 3D and 2D graphs as well as the influence of fractional parameter is also studied for some solutions. Our proposed results showed that improved $ \tan\big(\frac{\phi(\eta)}{2}\big) $-expansion method is reliable method to solve the nonlinear equation in mathematical physics.
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References
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Shahid Ali, Ahmad Javid. EXPLICIT SOLUTIONS FOR THE CONFORMABLE REGULARIZED LONG WAVE BURGER'S EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 344-358. doi: 10.11948/20220135
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Figure 1.
3D and corresponding 2D graph of
$ p_{1}(\eta) $ $ p=-1, \mu=1, s=1, S=1, q=1, \alpha=1, m=2, n=1, r=-3 $ -
Figure 2.
3D and corresponding 2D graphs of p3(η) with different values of fractional parameter α along side parameters p = −1, µ = 1, s = 1, S = 1, q = 1, m = 0, n = 3, r = −1.
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Figure 3.
3D and corresponding 2D graphs of
$ p_5(\eta) $ $ \alpha $ $ p=-1, \mu=1, s=1, S=1, q=1, m=1, n=3, r=2 $ -
Figure 4.
3D and corresponding 2D graphs depict the solution of
$ p_{7}(\eta) $ $ p=-1, \mu=1, s=1, \alpha=0.2, S=1, q=1, m=2, n=1, r=-1 $ -
Figure 5.
3D and corresponding 2D graphs depict the solution of
$ p_{13}(\eta) $ $ p=-1, \mu=1, s=1, \alpha=0.3, S=1, q=1, m=0, n=2, r=0 $