Browsing by Author "Khan, Arshad"

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Citation - WoS: 17
Citation - Scopus: 20
A high-order unconditionally stable numerical method for a class of multi-term time-fractional diffusion equation arising in the solute transport models
(Taylor & Francis Ltd, 2023) Alam, Mohammad Prawesh; Baleanu, Dumitru; Khan, Arshad; Baleanu, Dumitru; 56389; Matematik
In this paper, we study a high-order unconditionally stable numerical method to approximate the class of multi-term time-fractional diffusion equations. This type of problem appears in the modelling of transport of certain quantities such as heat, mass, energy, solutes in ground water and soils. The multi-term time-fractional derivative is approximated by using the Crank-Nicolson method for the Caputo's time derivative. The space derivative is approximated by using the collocation method based on quintic B-spline basis functions. We have established the stability and convergence analysis of the proposed numerical scheme thoroughly, and it is shown that the order of convergence in space variable is almost four and in the time variable is O (Delta t(2-max{gamma,gamma i})). To prove the accuracy and efficiency of the developed method, we consider four numerical examples and perform the numerical simulation. The developed algorithm works well andvalidate the theoretical results. The developed method is fourth-order convergent in the space variable, which is almost two orders of magnitude higher than the other spline collocation methods.
Citation - WoS: 32
Citation - Scopus: 31
Multiple bifurcation solitons, lumps and rogue waves solutions of a generalized perturbed KdV equation
(Springer, 2023) Khan, Arshad; Baleanu, Dumitru; Saifullah, Sayed; Ahmad, Shabir; Khan, Javed; Baleanu, Dumitru; 56389; Matematik
The perturbed KdV equation has many applications in mechanics and sound propagation in fluids. The aim of this manuscript is to study novel crucial exact solutions of the generalized perturbed KdV equation. The Hirota bilinear technique is implemented to derive general form solution of the considered equation. The novel soliton solutions are studied by taking different dispersion coefficients. We analyse first- and second-order soliton solutions, multiple-bifurcated soliton solutions, first- and second-order lump and rogue wave solutions of the considered equations. We show the effect of the parameters on the evolution of soliton solutions of the considered equation. All the obtained results are simulated by using MATLAB-2020.