Analysis of some generalized ABC – Fractional logistic models

Thabet Abdeljawad; Mohamed A. Hajji; Qasem M. Al-Mdallal; Fahd Jarad

doi:10.1016/j.aej.2020.01.030

Analysis of some generalized ABC – Fractional logistic models

Thabet Abdeljawad
, Mohamed A. Hajji
, Qasem M. Al-Mdallal
, Fahd Jarad

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

54 Citations (Scopus)

Abstract

In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilibrium points. Numerical illustrative examples are discussed for the studied models.

Original language	English
Pages (from-to)	2141-2148
Number of pages	8
Journal	Alexandria Engineering Journal
Volume	59
Issue number	4
DOIs	https://doi.org/10.1016/j.aej.2020.01.030
Publication status	Published - Aug 2020

Keywords

ABC – logistic equations
Generalized ABC – fractional derivatives
Generalized ABC – fractional integrals
Generalized Mittag-Leffler kernel
Modified ABC – logistic model

ASJC Scopus subject areas

General Engineering

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10.1016/j.aej.2020.01.030

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title = "Analysis of some generalized ABC – Fractional logistic models",

abstract = "In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilibrium points. Numerical illustrative examples are discussed for the studied models.",

keywords = "ABC – logistic equations, Generalized ABC – fractional derivatives, Generalized ABC – fractional integrals, Generalized Mittag-Leffler kernel, Modified ABC – logistic model",

author = "Thabet Abdeljawad and Hajji, \{Mohamed A.\} and Al-Mdallal, \{Qasem M.\} and Fahd Jarad",

note = "Publisher Copyright: {\textcopyright} 2020 Faculty of Engineering, Alexandria University",

year = "2020",

month = aug,

doi = "10.1016/j.aej.2020.01.030",

language = "English",

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journal = "Alexandria Engineering Journal",

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AU - Abdeljawad, Thabet

AU - Hajji, Mohamed A.

AU - Al-Mdallal, Qasem M.

AU - Jarad, Fahd

PY - 2020/8

Y1 - 2020/8

N2 - In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilibrium points. Numerical illustrative examples are discussed for the studied models.

AB - In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilibrium points. Numerical illustrative examples are discussed for the studied models.

KW - ABC – logistic equations

KW - Generalized ABC – fractional derivatives

KW - Generalized ABC – fractional integrals

KW - Generalized Mittag-Leffler kernel

KW - Modified ABC – logistic model

UR - https://www.scopus.com/pages/publications/85079900665

UR - https://www.scopus.com/pages/publications/85079900665#tab=citedBy

U2 - 10.1016/j.aej.2020.01.030

DO - 10.1016/j.aej.2020.01.030

M3 - Article

AN - SCOPUS:85079900665

SN - 1110-0168

VL - 59

SP - 2141

EP - 2148

JO - Alexandria Engineering Journal

JF - Alexandria Engineering Journal

IS - 4

ER -

Analysis of some generalized ABC – Fractional logistic models

Abstract

Keywords

ASJC Scopus subject areas

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