On the Approximate Solution of Fractional Logistic Differential Equation Using Operational Matrices of Bernstein Polynomials

Author(s)
R. F. Al-Bar

Affiliation(s)

Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia.

Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia.

Abstract

In this paper, operational matrices of Bernstein polynomials (BPs) are presented for solving the non-linear fractional Logistic differential equation (FLDE). The fractional derivative is described in the Riemann-Liouville sense. The operational matrices for the fractional integration in the Riemann-Liouville sense and the product are used to reduce FLDE to the solution of non-linear system of algebraic equations using Newton iteration method. Numerical results are introduced to satisfy the accuracy and the applicability of the proposed method.

In this paper, operational matrices of Bernstein polynomials (BPs) are presented for solving the non-linear fractional Logistic differential equation (FLDE). The fractional derivative is described in the Riemann-Liouville sense. The operational matrices for the fractional integration in the Riemann-Liouville sense and the product are used to reduce FLDE to the solution of non-linear system of algebraic equations using Newton iteration method. Numerical results are introduced to satisfy the accuracy and the applicability of the proposed method.

Keywords

Fractional Logistic Equation, Riemann-Liouville Fractional Derivatives, Riemann-Liouville Fractional Integral, Operational Matrix, Bernstein Polynomials

Fractional Logistic Equation, Riemann-Liouville Fractional Derivatives, Riemann-Liouville Fractional Integral, Operational Matrix, Bernstein Polynomials

Cite this paper

Al-Bar, R. (2015) On the Approximate Solution of Fractional Logistic Differential Equation Using Operational Matrices of Bernstein Polynomials.*Applied Mathematics*, **6**, 2096-2103. doi: 10.4236/am.2015.612184.

Al-Bar, R. (2015) On the Approximate Solution of Fractional Logistic Differential Equation Using Operational Matrices of Bernstein Polynomials.

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