Browsing by Author "Thabet H."

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An effective computational approach and sensitivity analysis to pseudo-parabolic-type equations
(2021-01-01) Kaplan M.; Butt A.R.; Thabet H.; Akbulut A.; Raza N.; Kumar D.
The researchers have developed numerous analytical and numerical techniques for solving fractional partial differential equations most of which provide approximate solutions. Exact solutions, however, are vitally important in a convenient conception of the qualitative properties of the concerned phenomena and processes. In this paper, the pseudo-parabolic-type equations with conformable fractional derivatives are reduced to conformable fractional nonlinear ordinary differential equations by implementing a simple wave transformation. An important benefit of the proposed transformation is that it yields analytical solutions of the conformable pseudo-parabolic type equations by applying the exponential rational function strategy. The sensitivity behaviour of the model has been mentioned thoroughly.
Solitary wave solutions and traveling wave solutions for systems of time-fractional nonlinear wave equations via an analytical approach
(2020-09-01) Thabet H.; Kendre S.; Peters J.; Kaplan M.
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.