Communications of the
Korean Mathematical Society CKMS

This paper presents an efficient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the efficiency of the method with different coefficients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

Keywords: numerical approximations, fractional shifted Legendre polynomial method, nonlinear fractional differential equation, population growth model, Caputo fractional derivative

MSC numbers: Primary 34A08, 74G10