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2 Fundamenta Informaticae

2 2019

2 Arqub O. A.

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Numerical Algorithm for the Solutions of Fractional Order Systems of Dirichlet Function Types with Comparative Analysis

100%

Arqub O. A.

2019

tom Vol. 166, nr 2

111--137

The aim of this article is to introduce the reproducing kernel algorithm for obtaining the numerical solutions of fractional order systems of Dirichlet function types. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n-term of exact solutions, numerical solutions of linear and nonlinear time-fractional equations of homogeneous and nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds for the present algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems compared with other numerical methods.

Application of Residual Power Series Method for the Solution of Time-fractional Schrödinger Equations in One-dimensional Space

100%

Arqub O. A.

2019

tom Vol. 166, nr 2

87--110

The object of this article is to present the computational solution of the time-fractional Schrödinger equation subject to given constraint condition based on the generalized Taylor series formula in the Caputo sense. The algorithm methodology is based on construct a multiple fractional power series solution in the form of a rabidly convergent series with minimum size of calculations using symbolic computation software. The proposed technique is fully compatible with the complexity of this problem and obtained results are highly encouraging. Efficacious computational experiments are provided to guarantee the procedure and to illustrate the theoretical statements of the present algorithm in order to show its potentiality, generality, and superiority for solving such fractional equation. Graphical results and numerical comparisons are presented and discussed quantitatively to illustrate the solution.