On the new double integral transform for solving singular system of hyperbolic equations
A. A. Alderremy
- Mathematics Department, Faculty of Science, King Kalied University, Abha, Saudi Arabia.
Tarig. M. Elzaki
- Mathematics Department, Faculty of Sciences and Arts-Alkamil, University of Jeddah, Jeddah, Saudi Arabia.
- Mathematics Department, Faculty of Science, Sudan University of Sciences and Technology, Sudan.
In this manuscript, we will introduce a new double transform called double Elzaki transform (modification of Smudu transform), where we will study this transform and their theorems on convergence. Also, we will discuss the double new transform and it is convergent. After that, we study the combination of this double transforms and the new method in order to solve the singular system of hyperbolic equations of anomalies in through the examples in this paper. We found that this method is very effective in solving these equations compared to other methods as they need only one step to get the exact solution, while the other methods need more steps.
Share and Cite
A. A. Alderremy, Tarig. M. Elzaki, On the new double integral transform for solving singular system of hyperbolic equations, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 10, 1207--1214
Alderremy A. A., Elzaki Tarig. M., On the new double integral transform for solving singular system of hyperbolic equations. J. Nonlinear Sci. Appl. (2018); 11(10):1207--1214
Alderremy, A. A., Elzaki, Tarig. M.. "On the new double integral transform for solving singular system of hyperbolic equations." Journal of Nonlinear Sciences and Applications, 11, no. 10 (2018): 1207--1214
- Double new integral
- nonlinear singular system of hyperbolic equations
J. Biazar, H. Ghazvini, Hes variational iteration method for solving linear and non-linear systems of ordinary differential equations, Appl. Math. Comput., 191 (2007), 287–297.
R. R. Dhunde, G. L. Waghmare, On Some Convergence Theorems of Double Laplace Transform, J. Inform. Math. Sci., 6 (2014), 45–54.
T. M. Elzaki , Application of Projected Differential Transform Method on Nonlinear Partial Differential Equations with Proportional Delay in One Variable, World Appl. Sci. J., 30 (2014), 345–349.
T. M. Elzaki , Double Laplace Variational Iteration Method for Solution of Nonlinear Convolution Partial Differential Equations, Arch. Sci., 65 (2012), 588–593.
T. M. Elzaki, J. Biazar, Homotopy Perturbation Method and Elzaki Transform for Solving System of Nonlinear Partial Differential Equations, World Appl. Sci. J., 24 (2013), 944–948.
T. M. Elzaki, S. M. Elzaki, E. A. Elnour, On the New Integral Transform Elzaki Transform Fundamental Properties Investigations and Applications, Global J. Math. Sci., 4 (2012), 1–13.
T. M. Elzaki, E. M. A. Hilal, Solution of Telegraph Equation by Modified of Double Sumudu Transform Elzaki Transform, Math. Theory Model., 2 (2012), 95–103.
J.-H. He, Variational iteration method for delay differential equations, Commun. Nonlinear Sci. Numer. Simul., 2 (1997), 235–236.
J.-H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Non-linear Mech., 34 (1999), 699–708.
J.-H. He, X.-H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl., 54 (2007), 881–894.
A. A. Hemeda, New iterative method: an application for solving fractional physical differential equations, Abstr. Appl. Anal., 2013 (2013), 9 pages.
E. Hesameddini, H. Latifizadeh, Reconstruction of variational iteration algorithms using the Laplace transform, Int. J. Nonlinear Sci. Num. Simul., 10 (2009), 1377–1382.
S. A. Khuri, A. Sayfy, A Laplace variational iteration strategy for the solution of differential equations, Appl. Math. Lett., 25 (2012), 2298–2305.
K. M. Saad , Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system, Eur. Phys. J. Plus, 133 (2018), 94 pages.
K. M. Saad, E. H. Al-Shareef, M. S. Mohamed, X. J. Yang, Optimal q-homotopy analysis method for time-space fractional gas dynamics equation, Eur. Phys. J. Plus, 132 (2017), 23 pages.
K. M. Saad, E. H. F. Al-Sharif, Analytical study for time and time-space fractional Burgers’ equation, Adv. Differ. Equ., 2017 (2017), 300 pages.
K. M. Saad, A. A. AL-Shomrani, An application of homotopy analysis transform method for Riccati differential equation of fractional order, J. Fract. Calc. Appl., 7 (2016), 61–72.
K. M. Saad, D. Baleanu, A. Atangana, New fractional derivatives applied to the Kortewegde Vries and Kortewegde VriesBurgers equations, Comp. Appl. Math., 2018 (2018), 14 pages.
G.-C. Wu, Challenge in the variational iteration method-a new approach to identification of the Lagrange mutipliers, J. King Saud Univ. Sci., 25 (2013), 175–178.
G.-C. Wu , Laplace transform Overcoming Principle Drawbacks in Application of the Variational Iteration Method to Fractional Heat Equations, Therm. Sci., 16 (2012), 1257–1261.
G.-C. Wu , Variational iteration method for solving the time-fractional diffusion equations in porous medium, Chin. Phys. B, 21 (2012), 120504.
G.-C. Wu, D. Baleanu , Variational iteration method for fractional calculus–a universal approach by Laplace transform, Adv. Differ. Equ., 2013 (2013), 18–27.
G.-C. Wu, D. Baleanu, Variational iteration method for the Burgers’ flow with fractional derivatives–New Lagrange multipliers, Appl. Math. Model., 37 (2012), 6183–6190.