Fitted Spectral Tau Jacobi Technique for Solving Certain Classes of Fractional Differential Equations

Authors

Abeer Adel Al-nana, Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, JordanFollow
Omar Abu Arqub, Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, JordanFollow
Mohammed Al-Smadi, Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanFollow
Nabil Shawagfeh, Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, JordanFollow

Author Country (or Countries)

Jordan

Abstract

In this paper, an efficient numerical technique, so-called the fitted spectral tau Jacobi (FSTJ), is presented to obtain the solutions of a class of fractional differential equations (FDEs) based on the Jacobi polynomials utilized as natural basis functions under the Caputo sense of fractional derivative. The solution methodology is based on the matrix-vector–product technique in Tau formulation of the model. A comparative study was conducted between the gained results in FSTJ method and other existing methods. Convergence and error analysis are presented to confirm the validity and feasibility of the proposed method for solving such problems. Numerical applications are given which refer to the efficiency and effectiveness of the FSTJ method.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/130611

Recommended Citation

Adel Al-nana, Abeer; Abu Arqub, Omar; Al-Smadi, Mohammed; and Shawagfeh, Nabil (2019) "Fitted Spectral Tau Jacobi Technique for Solving Certain Classes of Fractional Differential Equations," Applied Mathematics & Information Sciences: Vol. 13: Iss. 6, Article 11.
DOI: http://dx.doi.org/10.18576/amis/130611
Available at: https://digitalcommons.aaru.edu.jo/amis/vol13/iss6/11