Numerical Treatment for Solving Fractional Logistic Differential Equation

Abstract

This paper presents an accurate numerical method for solving fractional Logistic differential equation (FLDE). The fractional derivative in this problem is in the Caputo sense. The proposed method is so called fractional Chebyshev finite difference method. In this technique, we approximate FLDE with a finite dimensional problem. The method is based on the combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The Caputo fractional derivative is replaced by a difference quotient and the integral by a finite sum. The introduced method reduces the proposed problem for solving a system of algebraic equations, and by solving this system, we obtain the solution of FLDE. Special attention is given to study the convergence analysis and estimate an error upper bound of the obtained approximate formula. Illustrative examples are included to demonstrate the validity and the applicability of the proposed technique.