## International Journal of Differential Equations

### Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions

#### Abstract

In this article, an analytical reliable treatment based on the concept of residual error functions is employed to address the series solution of the differential logistic system in the fractional sense. The proposed technique is a combination of the generalized Taylor series and minimizing the residual error function. The solution methodology depends on the generation of a fractional expansion in an effective convergence formula, as well as on the optimization of truncated errors, ${\text{Res}}_{q}^{j}(t)$, through the use of repeated Caputo derivatives without any restrictive assumptions of system nature. To achieve this, some logistic patterns are tested to demonstrate the reliability and applicability of the suggested approach. Numerical comparison depicts that the proposed technique has high accuracy and less computational effect and is more efficient.

#### Article information

Source
Int. J. Differ. Equ., Volume 2019 (2019), Article ID 7609879, 11 pages.

Dates
Revised: 28 July 2019
Accepted: 25 August 2019
First available in Project Euclid: 17 October 2019

https://projecteuclid.org/euclid.ijde/1571277678

Digital Object Identifier
doi:10.1155/2019/7609879

Mathematical Reviews number (MathSciNet)
MR4015790

#### Citation

Alshammari, Saleh; Al-Smadi, Mohammed; Al Shammari, Mohammad; Hashim, Ishak; Alias, Mohd Almie. Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions. Int. J. Differ. Equ. 2019 (2019), Article ID 7609879, 11 pages. doi:10.1155/2019/7609879. https://projecteuclid.org/euclid.ijde/1571277678

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