Numerical approximations for Volterra’s population growth model with fractional order via a multi-domain pseudospectral method

On the numerical solution of a fractional population growth model

“…In Figure 2, solutions of the proposed method when γ = 1 are presented for different α values and N = 20. The solutions are valid when we compare with the findings in [5].…”

“…However, equation (1.6) has not been so far extensively studied except for a few papers (e.g., see [4,5]). An important contribution to the numerical approximation of fractional population model is the paper by Maleki et al [5]. They presented a multi-domain Legendre-Gauss pseudospectral method for approximate solutions of the fractional population model.…”

“…The analytical solution of equation (1.3) 5) shows that u(t) > 0 for all t when u 0 > 0. Problem (1.3)-(1.4) is studied extensively in the literature (see [2,3] and references therein).…”

An Efficient Approach of the Fractional Lagrange Interpolation

“…Recently, the fractional calculus has found in many real applications in science and engineering such as the control theory, fluid mechanics, bioengineering and biophysics (Dalir and Bashour, 2010;Grace, 2015;Jia et al, 2016;Maleki and Kajani, 2015;Soczkiewicz, 2002). Most of the fractional problems do not have analytical (exact) solutions, so, approximation and numerical techniques have been used (Grace, 2015;Garrappa, 2015;Jia et al, 2016;Khder, 2015).…”

Numerical Solution of Fractional Differential Equation System Using the Muntz-Legendre Polynomials

“…Moreover, this allows one to apply the fractional differential equations to model these phenomena more accurately. Some of these models and applications are presented in [1,2,3,4,5]. Also many researchers tried to investigate and describe these kinds of the equations (see Ref.…”