Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 8Citation - Scopus: 9Numerical Simulation for Generalized Time-Fractional Burgers' Equation With Three Distinct Linearization Schemes(Asme, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika; Reetika, ChawlaIn the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed nonlinear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.Article Citation - WoS: 16Citation - Scopus: 15On Numerical Solution of the Time Fractional Advection-Diffusion Equation Involving Atangana-Baleanu Derivative(Sciendo, 2019) Inc, Mustafa; Bayram, Mustafa; Baleanu, Dumitru; Partohaghighi, MohammadA powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): (ABC)D(0+)(,t)(beta)u(x, t) = zeta u(xx)(x, t) - kappa u(x)(x, t) + F(x, t), 0 < beta <= 1. The time-fractional derivative (ABC)D(0+)(,t)(beta)u(x, t) is described in the Atangana-Baleanu Caputo concept. The basis of our approach is transforming the original equation into a new equation by imposing a transformation involving a fictitious coordinate. Then, a geometric scheme namely the group preserving scheme (GPS) is implemented to solve the new equation by taking an initial guess. Moreover, in order to present the power of the presented approach some examples are solved, successfully.