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

• Published in: Fundamenta informaticae Vol. 166; no. 2; pp. 111 - 137
• Main Author: Abu Arqub, Omar
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2019; Sage Publications Ltd
• Subjects: Algorithms; Computer simulation; Dirichlet problem; Error analysis; Infinite series; Nonlinear equations; Numerical analysis; Numerical methods; Simulated annealing; Boundary value problems; Dirichlet function types; Comparative analysis; Reproducing kernel theory; Fractional order system; Numerical algorithm
• ISSN: 0169-2968; 1875-8681
• DOI: 10.3233/FI-2019-1796

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.