Global existence and uniqueness of solution of Atangana-Baleanu Caputo fractional differential equation with nonlinear term and approximate solutions
type: Item
instance of: scholarly article
title: Global existence and uniqueness of solution of Atangana-Baleanu Caputo fractional differential equation with nonlinear term and approximate solutions
zbMATH Open document ID: 1486.34027
DOI: 10.1155/2021/5675789
author: Meryeme Hassouna
author: E. H. El Kinani
author: Abdelaziz Ouhadan
published in: International Journal of Differential Equations
publication date: 2022-01-06T00:00:00Z
review text: Summary: In this paper, a class of fractional order differential equation expressed with Atangana-Baleanu Caputo derivative with nonlinear term is discussed. The existence and uniqueness of the solution of the general fractional differential equation are expressed. To present numerical results, we construct approximate scheme to be used for producing numerical solutions of the considered fractional differential equation. As an illustrative numerical example, we consider two Riccati fractional differential equations with different derivatives: Atangana-Baleanu Caputo and Caputo derivatives. Finally, the study of those examples verifies the theoretical results of global existence and uniqueness of solution. Moreover, numerical results underline the difference between solutions of both examples.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 7453302
Wikidata QID: Q115243674
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5675789
OpenAlex ID: W3178628201
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cites work: The fractional-order SIS epidemic model with variable population size
cites work: Volterra-type Lyapunov functions for fractional-order epidemic systems
cites work: On the solution of fractional order SIS epidemic model
cites work: On the stability of proliferation of kertinocytes in psoriatic skin fractional model
cites work: On the Fractional Calculus Model of Viscoelastic Behavior
cites work: On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative
cites work: Global existence theory and chaos control of fractional differential equations
cites work: The existence of a positive solution for a nonlinear fractional differential equation
cites work: Fractional differentiation matrices with applications
cites work: He's variational iteration method for solving fractional Riccati differential equation
cites work: Fractional variational iteration method and its application
cites work: Q5016733
cites work: Lie symmetry analysis and explicit solutions for the time-fractional regularized long-wave equation
cites work: Lyapunov functions for fractional order systems
cites work: Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems
cites work: Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models
cites work: Positive solutions of the fractional relaxation equation using lower and upper solutions
cites work: Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order
cites work: Q5699297
cites work: Analysis of fractional differential equations
cites work: Completely monotone generalized Mittag-Leffler functions
cites work: Detailed error analysis for a fractional Adams method
description: scientific article; zbMATH DE number 7453302