Numerical approximations to the nonlinear fractional-order logistic population model with fractional-order Bessel and Legendre bases. (English) Zbl 1498.65117
Summary: The main aim of this manuscript is to obtain the approximate solutions of the nonlinear Logistic equation of fractional order by developing a collocation approach based on the fractional-order Bessel and Legendre functions. The main characteristic of these polynomial approximation techniques is that they transform the governing differential equation into a system of algebraic equations, thus the computational efforts will be greatly reduced. Our secondary aim is to show a comparative investigation on the use of these fractional-order polynomials and to examine their utilities to solve the model problem. Numerical experiments are carried out to demonstrate the validity and applicability of the presented techniques and comparisons are made with methods available in the standard literature. The methods perform very well in terms of efficiency and simplicity to solve this population model especially when the Legendre bases are utilized.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 92D25 | Population dynamics (general) |
Keywords:
Bessel functions; collocation scheme; fractional Liouville-Caputo derivative; Legendre functions; logistic differential equationReferences:
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