Advanced analytical treatment of fractional logistic equations based on residual error functions
type: Item
instance of: scholarly article
title: Advanced analytical treatment of fractional logistic equations based on residual error functions
zbMATH Open document ID: 1447.34008
DOI: 10.1155/2019/7609879
author: Saleh Alshammari
author: Mohammed H. Al-Smadi
author: M. Alshammari
author: Mohd Almie Alias
author: I. Hashim
published in: International Journal of Differential Equations
publication date: 2020-07-03T00:00:00Z
review text: Summary: In this article, an analytical 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 applicability of the suggested approach. Numerical comparison depicts that the proposed technique has high accuracy and less computational effect and is more efficient.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 7217330
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/7609879
OpenAlex ID: W2976139966
cites work: Q3864730
cites work: Q4233638
cites work: Computational algorithm for solving Fredholm time-fractional partial integrodifferential equations of Dirichlet functions type with error estimates
cites work: Atangana-Baleanu fractional approach to the solutions of Bagley-Torvik and Painlevé equations in Hilbert space
cites work: Numerical Multistep Approach for Solving Fractional Partial Differential Equations
cites work: Numerical investigation for handling fractional-order Rabinovich-Fabrikant model using the multistep approach
cites work: Q2970935
cites work: Numerical solutions of fractional systems of two-point BVPs by using the iterative reproducing kernel algorithm
cites work: Solving fractional-order logistic equation using a new iterative method
cites work: On approximate solutions for fractional logistic differential equation
cites work: Numerical studies for fractional-order logistic differential equation with two different delays
cites work: A novel representation of the exact solution for differential algebraic equations system using residual power-series method
cites work: Computational optimization of residual power series algorithm for certain classes of fuzzy fractional differential equations
cites work: A general form of the generalized Taylor's formula with some applications
cites work: Two computational approaches for solving a fractional obstacle system in Hilbert space
cites work: Construction of fractional power series solutions to fractional stiff system using residual functions algorithm
cites work: An analytical numerical method for solving fuzzy fractional Volterra integro-differential equations
cites work: Q3114367
cites work: A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations
cites work: Solutions of nonlinear systems by reproducing kernel method
cites work: Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method
cites work: Reliable numerical algorithm for handling fuzzy integral equations of second kind in Hilbert spaces
cites work: A numerical iterative method for solving systems of first-order periodic boundary value problems
cites work: Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique
cites work: Iterative reproducing kernel method for solving second-order integrodifferential equations of Fredholm type
cites work: On solutions of variable-order fractional differential equations
description: scientific article; zbMATH DE number 7217330